Best Known (94−41, 94, s)-Nets in Base 16
(94−41, 94, 526)-Net over F16 — Constructive and digital
Digital (53, 94, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 47, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(94−41, 94, 734)-Net over F16 — Digital
Digital (53, 94, 734)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1694, 734, F16, 41) (dual of [734, 640, 42]-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(1686, 642, F16, 41) (dual of [642, 556, 42]-code), using
- trace code [i] based on linear OA(25643, 321, F256, 41) (dual of [321, 278, 42]-code), using
- extended algebraic-geometric code AGe(F,279P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25643, 321, F256, 41) (dual of [321, 278, 42]-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(1686, 642, F16, 41) (dual of [642, 556, 42]-code), using
(94−41, 94, 219963)-Net in Base 16 — Upper bound on s
There is no (53, 94, 219964)-net in base 16, because
- 1 times m-reduction [i] would yield (53, 93, 219964)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 9619 677339 555865 199211 667762 260313 695573 334409 163985 903159 295094 611638 333200 663611 433866 570483 016074 916721 524826 > 1693 [i]