Best Known (90−39, 90, s)-Nets in Base 16
(90−39, 90, 526)-Net over F16 — Constructive and digital
Digital (51, 90, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 45, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(90−39, 90, 735)-Net over F16 — Digital
Digital (51, 90, 735)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1690, 735, F16, 39) (dual of [735, 645, 40]-code), using
- 85 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0, 1, 38 times 0) [i] based on linear OA(1682, 642, F16, 39) (dual of [642, 560, 40]-code), using
- trace code [i] based on linear OA(25641, 321, F256, 39) (dual of [321, 280, 40]-code), using
- extended algebraic-geometric code AGe(F,281P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25641, 321, F256, 39) (dual of [321, 280, 40]-code), using
- 85 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0, 1, 38 times 0) [i] based on linear OA(1682, 642, F16, 39) (dual of [642, 560, 40]-code), using
(90−39, 90, 230917)-Net in Base 16 — Upper bound on s
There is no (51, 90, 230918)-net in base 16, because
- 1 times m-reduction [i] would yield (51, 89, 230918)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 146792 584364 823075 929315 279352 003373 989308 152937 875585 177697 220292 514066 120317 538972 215403 937145 311416 145856 > 1689 [i]