Best Known (76−50, 76, s)-Nets in Base 16
(76−50, 76, 65)-Net over F16 — Constructive and digital
Digital (26, 76, 65)-net over F16, using
- t-expansion [i] based on digital (6, 76, 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
(76−50, 76, 104)-Net in Base 16 — Constructive
(26, 76, 104)-net in base 16, using
- 9 times m-reduction [i] based on (26, 85, 104)-net in base 16, using
- base change [i] based on digital (9, 68, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- base change [i] based on digital (9, 68, 104)-net over F32, using
(76−50, 76, 150)-Net over F16 — Digital
Digital (26, 76, 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
(76−50, 76, 3091)-Net in Base 16 — Upper bound on s
There is no (26, 76, 3092)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 32 768276 621551 017083 772732 374422 992769 029479 716895 972342 852054 508794 084895 108522 027240 021376 > 1676 [i]