Best Known (42−25, 42, s)-Nets in Base 256
(42−25, 42, 519)-Net over F256 — Constructive and digital
Digital (17, 42, 519)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 14, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (3, 28, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- digital (2, 14, 259)-net over F256, using
(42−25, 42, 716)-Net over F256 — Digital
Digital (17, 42, 716)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25642, 716, F256, 25) (dual of [716, 674, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(25642, 771, F256, 25) (dual of [771, 729, 26]-code), using
(42−25, 42, 3507306)-Net in Base 256 — Upper bound on s
There is no (17, 42, 3507307)-net in base 256, because
- 1 times m-reduction [i] would yield (17, 41, 3507307)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 546 812995 832092 016463 261216 934096 809462 702694 309668 500290 635069 420853 976861 913690 051686 847488 607496 > 25641 [i]