Best Known (26, 26+34, s)-Nets in Base 16
(26, 26+34, 103)-Net over F16 — Constructive and digital
Digital (26, 60, 103)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (3, 20, 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, 40, 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, 20, 38)-net over F16, using
(26, 26+34, 129)-Net in Base 16 — Constructive
(26, 60, 129)-net in base 16, using
- base change [i] based on (6, 40, 129)-net in base 64, using
- 2 times m-reduction [i] based on (6, 42, 129)-net in base 64, 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
- base change [i] based on digital (0, 36, 129)-net over F128, using
- 2 times m-reduction [i] based on (6, 42, 129)-net in base 64, using
(26, 26+34, 150)-Net over F16 — Digital
Digital (26, 60, 150)-net over F16, using
- net from sequence [i] based on digital (26, 149)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 26 and N(F) ≥ 150, using
(26, 26+34, 161)-Net in Base 16
(26, 60, 161)-net in base 16, using
- base change [i] based on digital (6, 40, 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
(26, 26+34, 8496)-Net in Base 16 — Upper bound on s
There is no (26, 60, 8497)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 769814 870383 255201 745872 607247 941590 191263 787436 053928 666006 031665 963536 > 1660 [i]