The match with Surrey was abandoned after a horrible collision between Surrey fielders Moises Henriques and Rory Burns, with both taken by ambulance to hospital.
Fans at the game will be able watch a County Championship or Royal London One Day Cup group game, subject to availability.
A statement from Sussex chief executive Zac Toumazi read: “Sussex County Cricket Club would like to express their appreciation for the supportive attitude of the crowd towards the unfortunate accident at Arundel Castle Cricket Club which caused the match to be abandoned.
“We are pleased to advise that Moises Henriques and Rory Burns are recovering well following prompt treatment for their injuries.
“Due to the circumstances that resulted in the match being abandoned, and as a gesture of goodwill and appreciation, Sussex County Cricket Club would like to offer all customers who have a paid ticket, the opportunity to attend a future LV=County Championship or Royal London One Day Cup group game in 2015, subject to availability.”
Toumazi added that a new layout was tried for the game and said: “This year, we tried a new layout at Arundel following feedback from previous years.
“This resulted in improved spectator views by taking advantage of the natural bank. However, we recognise that the bar facilities did not cope with the volume placed on them and we have learned lessons from this.
“We apologise for any inconvenience caused, and remain committed to continually improving our spectator experience.
“Thank you once again for your support at Arundel and for the remainder of the season ahead.”
To attend another match, Sussex said in the statement: “You may not use the original ticket for entry for a future match.
“If your ticket was purchased online or over the phone before Sunday, June 14, you may phone 0844 264 0206 to obtain your replacement ticket
“All tickets purchased on the gate must either be returned by post or in person to the Club Shop. These tickets must be returned to the ticket office and a new ticket issued
“The replacement ticket issued will be the “best available”.”
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