Best Known (75−32, 75, s)-Nets in Base 16
(75−32, 75, 524)-Net over F16 — Constructive and digital
Digital (43, 75, 524)-net over F16, using
- 1 times m-reduction [i] based on digital (43, 76, 524)-net over F16, using
- trace code for nets [i] based on digital (5, 38, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- trace code for nets [i] based on digital (5, 38, 262)-net over F256, using
(75−32, 75, 707)-Net over F16 — Digital
Digital (43, 75, 707)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1675, 707, F16, 32) (dual of [707, 632, 33]-code), using
- 58 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 5 times 0, 1, 15 times 0, 1, 32 times 0) [i] based on linear OA(1668, 642, F16, 32) (dual of [642, 574, 33]-code), using
- trace code [i] based on linear OA(25634, 321, F256, 32) (dual of [321, 287, 33]-code), using
- extended algebraic-geometric code AGe(F,288P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25634, 321, F256, 32) (dual of [321, 287, 33]-code), using
- 58 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 5 times 0, 1, 15 times 0, 1, 32 times 0) [i] based on linear OA(1668, 642, F16, 32) (dual of [642, 574, 33]-code), using
(75−32, 75, 199867)-Net in Base 16 — Upper bound on s
There is no (43, 75, 199868)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 037185 804419 776465 481396 710221 809328 663952 674198 881372 801859 186388 012205 571340 776380 435321 > 1675 [i]