Best Known (96−42, 96, s)-Nets in Base 16
(96−42, 96, 526)-Net over F16 — Constructive and digital
Digital (54, 96, 526)-net over F16, using
- trace code for nets [i] based on digital (6, 48, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(96−42, 96, 733)-Net over F16 — Digital
Digital (54, 96, 733)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1696, 733, F16, 42) (dual of [733, 637, 43]-code), using
- 83 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0, 1, 36 times 0) [i] based on linear OA(1688, 642, F16, 42) (dual of [642, 554, 43]-code), using
- trace code [i] based on linear OA(25644, 321, F256, 42) (dual of [321, 277, 43]-code), using
- extended algebraic-geometric code AGe(F,278P) [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- trace code [i] based on linear OA(25644, 321, F256, 42) (dual of [321, 277, 43]-code), using
- 83 step Varšamov–Edel lengthening with (ri) = (4, 0, 1, 5 times 0, 1, 12 times 0, 1, 24 times 0, 1, 36 times 0) [i] based on linear OA(1688, 642, F16, 42) (dual of [642, 554, 43]-code), using
(96−42, 96, 184894)-Net in Base 16 — Upper bound on s
There is no (54, 96, 184895)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 39 406088 491650 272236 002645 333285 649227 282788 473643 295246 388754 932330 806036 200986 953781 121113 530605 209461 739464 176926 > 1696 [i]