Best Known (89−36, 89, s)-Nets in Base 16
(89−36, 89, 530)-Net over F16 — Constructive and digital
Digital (53, 89, 530)-net over F16, using
- 1 times m-reduction [i] based on digital (53, 90, 530)-net over F16, using
- trace code for nets [i] based on digital (8, 45, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
- trace code for nets [i] based on digital (8, 45, 265)-net over F256, using
(89−36, 89, 1089)-Net over F16 — Digital
Digital (53, 89, 1089)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1689, 1089, F16, 36) (dual of [1089, 1000, 37]-code), using
- 62 step Varšamov–Edel lengthening with (ri) = (1, 61 times 0) [i] based on linear OA(1688, 1026, F16, 36) (dual of [1026, 938, 37]-code), using
- trace code [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
- trace code [i] based on linear OA(25644, 513, F256, 36) (dual of [513, 469, 37]-code), using
- 62 step Varšamov–Edel lengthening with (ri) = (1, 61 times 0) [i] based on linear OA(1688, 1026, F16, 36) (dual of [1026, 938, 37]-code), using
(89−36, 89, 452620)-Net in Base 16 — Upper bound on s
There is no (53, 89, 452621)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 146789 086210 651022 353403 594462 668495 094735 520389 871146 389776 849087 909652 869701 836347 022346 468894 402886 820096 > 1689 [i]