Best Known (21, 47, s)-Nets in Base 16
(21, 47, 98)-Net over F16 — Constructive and digital
Digital (21, 47, 98)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 15, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- digital (6, 32, 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 (2, 15, 33)-net over F16, using
(21, 47, 129)-Net in Base 16 — Constructive
(21, 47, 129)-net in base 16, using
- 2 times m-reduction [i] based on (21, 49, 129)-net in base 16, using
- base change [i] based on digital (0, 28, 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, 28, 129)-net over F128, using
(21, 47, 130)-Net over F16 — Digital
Digital (21, 47, 130)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(1647, 130, F16, 2, 26) (dual of [(130, 2), 213, 27]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(1645, 129, F16, 2, 26) (dual of [(129, 2), 213, 27]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,231P) [i] based on function field F/F16 with g(F) = 19 and N(F) ≥ 129, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(1645, 129, F16, 2, 26) (dual of [(129, 2), 213, 27]-NRT-code), using
(21, 47, 133)-Net in Base 16
(21, 47, 133)-net in base 16, using
- 1 times m-reduction [i] based on (21, 48, 133)-net in base 16, using
- base change [i] based on digital (5, 32, 133)-net over F64, using
- net from sequence [i] based on digital (5, 132)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 133, using
- net from sequence [i] based on digital (5, 132)-sequence over F64, using
- base change [i] based on digital (5, 32, 133)-net over F64, using
(21, 47, 8517)-Net in Base 16 — Upper bound on s
There is no (21, 47, 8518)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 392 503752 800944 558832 832987 797757 294887 959131 162825 718936 > 1647 [i]