Best Known (92−40, 92, s)-Nets in Base 16
(92−40, 92, 526)-Net over F16 — Constructive and digital
Digital (52, 92, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 46, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(92−40, 92, 734)-Net over F16 — Digital
Digital (52, 92, 734)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1692, 734, F16, 40) (dual of [734, 642, 41]-code), using
- 84 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0, 1, 37 times 0) [i] based on linear OA(1684, 642, F16, 40) (dual of [642, 558, 41]-code), using
- trace code [i] based on linear OA(25642, 321, F256, 40) (dual of [321, 279, 41]-code), using
- extended algebraic-geometric code AGe(F,280P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25642, 321, F256, 40) (dual of [321, 279, 41]-code), using
- 84 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0, 1, 37 times 0) [i] based on linear OA(1684, 642, F16, 40) (dual of [642, 558, 41]-code), using
(92−40, 92, 191488)-Net in Base 16 — Upper bound on s
There is no (52, 92, 191489)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 601 268654 483971 209450 104887 905965 747598 391838 286128 459985 707814 351722 706603 453984 118384 330861 067293 417404 088576 > 1692 [i]