Best Known (22, 53, s)-Nets in Base 256
(22, 53, 521)-Net over F256 — Constructive and digital
Digital (22, 53, 521)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (3, 18, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- digital (4, 35, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- digital (3, 18, 260)-net over F256, using
(22, 53, 865)-Net over F256 — Digital
Digital (22, 53, 865)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25653, 865, F256, 31) (dual of [865, 812, 32]-code), using
- 338 step Varšamov–Edel lengthening with (ri) = (8, 0, 0, 1, 6 times 0, 1, 13 times 0, 1, 28 times 0, 1, 55 times 0, 1, 93 times 0, 1, 134 times 0) [i] based on linear OA(25639, 513, F256, 31) (dual of [513, 474, 32]-code), using
- extended algebraic-geometric code AGe(F,481P) [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,481P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- 338 step Varšamov–Edel lengthening with (ri) = (8, 0, 0, 1, 6 times 0, 1, 13 times 0, 1, 28 times 0, 1, 55 times 0, 1, 93 times 0, 1, 134 times 0) [i] based on linear OA(25639, 513, F256, 31) (dual of [513, 474, 32]-code), using
(22, 53, 5620709)-Net in Base 256 — Upper bound on s
There is no (22, 53, 5620710)-net in base 256, because
- 1 times m-reduction [i] would yield (22, 52, 5620710)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 169230 623254 351138 963216 309152 954915 266501 101129 404495 530370 335989 669658 680511 924630 722524 655790 457062 941738 337306 014839 591376 > 25652 [i]