Best Known (59−34, 59, s)-Nets in Base 256
(59−34, 59, 522)-Net over F256 — Constructive and digital
Digital (25, 59, 522)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (4, 21, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- digital (4, 38, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256 (see above)
- digital (4, 21, 261)-net over F256, using
(59−34, 59, 1069)-Net over F256 — Digital
Digital (25, 59, 1069)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25659, 1069, F256, 34) (dual of [1069, 1010, 35]-code), using
- 43 step Varšamov–Edel lengthening with (ri) = (1, 42 times 0) [i] based on linear OA(25658, 1025, F256, 34) (dual of [1025, 967, 35]-code), using
- extended algebraic-geometric code AGe(F,990P) [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025, using
- K1,2 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,990P) [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025, using
- 43 step Varšamov–Edel lengthening with (ri) = (1, 42 times 0) [i] based on linear OA(25658, 1025, F256, 34) (dual of [1025, 967, 35]-code), using
(59−34, 59, 6418207)-Net in Base 256 — Upper bound on s
There is no (25, 59, 6418208)-net in base 256, because
- the generalized Rao bound for nets shows that 256m ≥ 12194 337739 396441 368061 534195 611782 955745 612935 309777 665016 277286 086487 948987 271667 626733 432346 436689 990873 956013 817310 346778 857948 648851 305331 > 25659 [i]