Best Known (24, 54, s)-Nets in Base 16
(24, 54, 103)-Net over F16 — Constructive and digital
Digital (24, 54, 103)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (3, 18, 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, 36, 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, 18, 38)-net over F16, using
(24, 54, 129)-Net in Base 16 — Constructive
(24, 54, 129)-net in base 16, using
- 2 times m-reduction [i] based on (24, 56, 129)-net in base 16, using
- base change [i] based on digital (0, 32, 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
- base change [i] based on digital (0, 32, 129)-net over F128, using
(24, 54, 133)-Net over F16 — Digital
Digital (24, 54, 133)-net over F16, using
(24, 54, 161)-Net in Base 16
(24, 54, 161)-net in base 16, using
- base change [i] based on digital (6, 36, 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
(24, 54, 9249)-Net in Base 16 — Upper bound on s
There is no (24, 54, 9250)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 105347 842269 689571 619604 057091 567233 544170 799749 868906 999759 159376 > 1654 [i]