Best Known (31, 31+76, s)-Nets in Base 16
(31, 31+76, 65)-Net over F16 — Constructive and digital
Digital (31, 107, 65)-net over F16, using
- t-expansion [i] based on digital (6, 107, 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
(31, 31+76, 104)-Net in Base 16 — Constructive
(31, 107, 104)-net in base 16, using
- 3 times m-reduction [i] based on (31, 110, 104)-net in base 16, using
- base change [i] based on digital (9, 88, 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, 88, 104)-net over F32, using
(31, 31+76, 168)-Net over F16 — Digital
Digital (31, 107, 168)-net over F16, using
- net from sequence [i] based on digital (31, 167)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 31 and N(F) ≥ 168, using
(31, 31+76, 2440)-Net in Base 16 — Upper bound on s
There is no (31, 107, 2441)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 694 732469 465388 272244 140019 053306 510819 660273 271608 224903 812366 095678 041111 284795 365497 961047 233055 214698 461630 184764 756926 885296 > 16107 [i]