Best Known (57, 57+40, s)-Nets in Base 16
(57, 57+40, 530)-Net over F16 — Constructive and digital
Digital (57, 97, 530)-net over F16, using
- 1 times m-reduction [i] based on digital (57, 98, 530)-net over F16, using
- trace code for nets [i] based on digital (8, 49, 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, 49, 265)-net over F256, using
(57, 57+40, 1048)-Net over F16 — Digital
Digital (57, 97, 1048)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1697, 1048, F16, 40) (dual of [1048, 951, 41]-code), using
- 21 step Varšamov–Edel lengthening with (ri) = (1, 20 times 0) [i] based on linear OA(1696, 1026, F16, 40) (dual of [1026, 930, 41]-code), using
- trace code [i] based on linear OA(25648, 513, F256, 40) (dual of [513, 465, 41]-code), using
- extended algebraic-geometric code AGe(F,472P) [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,472P) [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- trace code [i] based on linear OA(25648, 513, F256, 40) (dual of [513, 465, 41]-code), using
- 21 step Varšamov–Edel lengthening with (ri) = (1, 20 times 0) [i] based on linear OA(1696, 1026, F16, 40) (dual of [1026, 930, 41]-code), using
(57, 57+40, 382987)-Net in Base 16 — Upper bound on s
There is no (57, 97, 382988)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 630 448453 106430 944029 637485 005342 930077 597809 058473 389058 249489 561928 807099 929312 605284 115834 080905 836425 425717 739776 > 1697 [i]