Best Known (41−26, 41, s)-Nets in Base 16
(41−26, 41, 65)-Net over F16 — Constructive and digital
Digital (15, 41, 65)-net over F16, using
- t-expansion [i] based on digital (6, 41, 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
(41−26, 41, 80)-Net in Base 16 — Constructive
(15, 41, 80)-net in base 16, using
- 1 times m-reduction [i] based on (15, 42, 80)-net in base 16, using
- base change [i] based on digital (1, 28, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- base change [i] based on digital (1, 28, 80)-net over F64, using
(41−26, 41, 98)-Net over F16 — Digital
Digital (15, 41, 98)-net over F16, using
- net from sequence [i] based on digital (15, 97)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 15 and N(F) ≥ 98, using
(41−26, 41, 2364)-Net in Base 16 — Upper bound on s
There is no (15, 41, 2365)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 23 499953 450258 525241 828060 800808 947809 557879 302176 > 1641 [i]