Best Known (15, 15+57, s)-Nets in Base 16
(15, 15+57, 65)-Net over F16 — Constructive and digital
Digital (15, 72, 65)-net over F16, using
- t-expansion [i] based on digital (6, 72, 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
(15, 15+57, 98)-Net over F16 — Digital
Digital (15, 72, 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
(15, 15+57, 836)-Net in Base 16 — Upper bound on s
There is no (15, 72, 837)-net in base 16, because
- 1 times m-reduction [i] would yield (15, 71, 837)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 31 839355 090002 356994 676858 474056 042862 105843 750028 722475 708294 899030 918675 957317 085816 > 1671 [i]