Best Known (27, 61, s)-Nets in Base 16
(27, 61, 110)-Net over F16 — Constructive and digital
Digital (27, 61, 110)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (4, 21, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- net from sequence [i] based on digital (4, 44)-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 (4, 21, 45)-net over F16, using
(27, 61, 129)-Net in Base 16 — Constructive
(27, 61, 129)-net in base 16, using
- 2 times m-reduction [i] based on (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
- base change [i] based on digital (0, 36, 129)-net over F128, using
(27, 61, 156)-Net over F16 — Digital
Digital (27, 61, 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, 61, 161)-Net in Base 16
(27, 61, 161)-net in base 16, using
- 2 times m-reduction [i] based on (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
- base change [i] based on digital (6, 42, 161)-net over F64, using
(27, 61, 10002)-Net in Base 16 — Upper bound on s
There is no (27, 61, 10003)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 28 277037 673180 147128 977464 639961 181174 846543 553898 658123 876348 885720 634366 > 1661 [i]