Best Known (99−33, 99, s)-Nets in Base 16
(99−33, 99, 1028)-Net over F16 — Constructive and digital
Digital (66, 99, 1028)-net over F16, using
- 161 times duplication [i] based on digital (65, 98, 1028)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (16, 32, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 16, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 16, 257)-net over F256, using
- digital (33, 66, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 33, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- trace code for nets [i] based on digital (0, 33, 257)-net over F256, using
- digital (16, 32, 514)-net over F16, using
- (u, u+v)-construction [i] based on
(99−33, 99, 4597)-Net over F16 — Digital
Digital (66, 99, 4597)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1699, 4597, F16, 33) (dual of [4597, 4498, 34]-code), using
- 492 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 9 times 0, 1, 24 times 0, 1, 61 times 0, 1, 136 times 0, 1, 254 times 0) [i] based on linear OA(1691, 4097, F16, 33) (dual of [4097, 4006, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 492 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 1, 9 times 0, 1, 24 times 0, 1, 61 times 0, 1, 136 times 0, 1, 254 times 0) [i] based on linear OA(1691, 4097, F16, 33) (dual of [4097, 4006, 34]-code), using
(99−33, 99, large)-Net in Base 16 — Upper bound on s
There is no (66, 99, large)-net in base 16, because
- 31 times m-reduction [i] would yield (66, 68, large)-net in base 16, but