Best Known (86−59, 86, s)-Nets in Base 16
(86−59, 86, 65)-Net over F16 — Constructive and digital
Digital (27, 86, 65)-net over F16, using
- t-expansion [i] based on digital (6, 86, 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
(86−59, 86, 104)-Net in Base 16 — Constructive
(27, 86, 104)-net in base 16, using
- 4 times m-reduction [i] based on (27, 90, 104)-net in base 16, using
- base change [i] based on digital (9, 72, 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, 72, 104)-net over F32, using
(86−59, 86, 156)-Net over F16 — Digital
Digital (27, 86, 156)-net over F16, using
- net from sequence [i] based on digital (27, 155)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 27 and N(F) ≥ 156, using
(86−59, 86, 2616)-Net in Base 16 — Upper bound on s
There is no (27, 86, 2617)-net in base 16, because
- 1 times m-reduction [i] would yield (27, 85, 2617)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 2 252930 910731 411783 364353 884166 113544 906626 883026 313837 878669 749605 626526 086948 681634 885687 163059 977696 > 1685 [i]