Best Known (57−38, 57, s)-Nets in Base 16
(57−38, 57, 65)-Net over F16 — Constructive and digital
Digital (19, 57, 65)-net over F16, using
- t-expansion [i] based on digital (6, 57, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(57−38, 57, 98)-Net in Base 16 — Constructive
(19, 57, 98)-net in base 16, using
- 3 times m-reduction [i] based on (19, 60, 98)-net in base 16, using
- base change [i] based on digital (7, 48, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- base change [i] based on digital (7, 48, 98)-net over F32, using
(57−38, 57, 129)-Net over F16 — Digital
Digital (19, 57, 129)-net over F16, using
- net from sequence [i] based on digital (19, 128)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 19 and N(F) ≥ 129, using
(57−38, 57, 2154)-Net in Base 16 — Upper bound on s
There is no (19, 57, 2155)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 431 825192 256448 352954 784477 446269 624433 016368 976294 673263 916212 368176 > 1657 [i]