Best Known (71−58, 71, s)-Nets in Base 16
(71−58, 71, 65)-Net over F16 — Constructive and digital
Digital (13, 71, 65)-net over F16, using
- t-expansion [i] based on digital (6, 71, 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
(71−58, 71, 97)-Net over F16 — Digital
Digital (13, 71, 97)-net over F16, using
- net from sequence [i] based on digital (13, 96)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 13 and N(F) ≥ 97, using
(71−58, 71, 674)-Net in Base 16 — Upper bound on s
There is no (13, 71, 675)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 31 774705 775776 180759 932375 968848 167388 497335 748868 973001 519107 614576 273447 673967 927376 > 1671 [i]