Best Known (25, 25+32, s)-Nets in Base 16
(25, 25+32, 103)-Net over F16 — Constructive and digital
Digital (25, 57, 103)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (3, 19, 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, 38, 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, 19, 38)-net over F16, using
(25, 25+32, 129)-Net in Base 16 — Constructive
(25, 57, 129)-net in base 16, using
- 161 times duplication [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
(25, 25+32, 144)-Net over F16 — Digital
Digital (25, 57, 144)-net over F16, using
- net from sequence [i] based on digital (25, 143)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 25 and N(F) ≥ 144, using
(25, 25+32, 161)-Net in Base 16
(25, 57, 161)-net in base 16, using
- base change [i] based on digital (6, 38, 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
(25, 25+32, 8824)-Net in Base 16 — Upper bound on s
There is no (25, 57, 8825)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 431 535274 404171 700323 314675 020939 501533 511921 405589 402127 323635 255501 > 1657 [i]