Best Known (13, 13+72, s)-Nets in Base 16
(13, 13+72, 65)-Net over F16 — Constructive and digital
Digital (13, 85, 65)-net over F16, using
- t-expansion [i] based on digital (6, 85, 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
(13, 13+72, 97)-Net over F16 — Digital
Digital (13, 85, 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
(13, 13+72, 643)-Net in Base 16 — Upper bound on s
There is no (13, 85, 644)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 296000 236022 328510 646571 542451 038293 357806 469738 206051 516180 496459 937281 247666 119789 744192 534181 327136 > 1685 [i]