Best Known (27, 27+36, s)-Nets in Base 16
(27, 27+36, 103)-Net over F16 — Constructive and digital
Digital (27, 63, 103)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (3, 21, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- digital (6, 42, 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
- digital (3, 21, 38)-net over F16, using
(27, 27+36, 129)-Net in Base 16 — Constructive
(27, 63, 129)-net in base 16, using
- base change [i] based on digital (0, 36, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
(27, 27+36, 156)-Net over F16 — Digital
Digital (27, 63, 156)-net over F16, using
- net from sequence [i] based on digital (27, 155)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 27 and N(F) ≥ 156, using
(27, 27+36, 161)-Net in Base 16
(27, 63, 161)-net in base 16, using
- base change [i] based on digital (6, 42, 161)-net over F64, using
- net from sequence [i] based on digital (6, 160)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 6 and N(F) ≥ 161, using
- net from sequence [i] based on digital (6, 160)-sequence over F64, using
(27, 27+36, 8240)-Net in Base 16 — Upper bound on s
There is no (27, 63, 8241)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 7246 581494 869916 925724 135208 094546 136661 989277 807607 644679 158879 453646 756496 > 1663 [i]