Best Known (59−36, 59, s)-Nets in Base 256
(59−36, 59, 519)-Net over F256 — Constructive and digital
Digital (23, 59, 519)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 20, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (3, 39, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- digital (2, 20, 259)-net over F256, using
(59−36, 59, 663)-Net over F256 — Digital
Digital (23, 59, 663)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25659, 663, F256, 36) (dual of [663, 604, 37]-code), using
- 135 step Varšamov–Edel lengthening with (ri) = (10, 0, 0, 1, 4 times 0, 1, 10 times 0, 1, 19 times 0, 1, 35 times 0, 1, 59 times 0) [i] based on linear OA(25644, 513, F256, 36) (dual of [513, 469, 37]-code), using
- extended algebraic-geometric code AGe(F,476P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- extended algebraic-geometric code AGe(F,476P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- 135 step Varšamov–Edel lengthening with (ri) = (10, 0, 0, 1, 4 times 0, 1, 10 times 0, 1, 19 times 0, 1, 35 times 0, 1, 59 times 0) [i] based on linear OA(25644, 513, F256, 36) (dual of [513, 469, 37]-code), using
(59−36, 59, 2318802)-Net in Base 256 — Upper bound on s
There is no (23, 59, 2318803)-net in base 256, because
- the generalized Rao bound for nets shows that 256m ≥ 12194 401374 837980 174778 391506 043091 864642 389418 469696 759311 210889 453365 410424 578323 463270 006099 698562 993733 448114 988560 458617 522645 811028 491221 > 25659 [i]