Best Known (87−71, 87, s)-Nets in Base 16
(87−71, 87, 65)-Net over F16 — Constructive and digital
Digital (16, 87, 65)-net over F16, using
- t-expansion [i] based on digital (6, 87, 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
(87−71, 87, 98)-Net over F16 — Digital
Digital (16, 87, 98)-net over F16, using
- t-expansion [i] based on digital (15, 87, 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
- net from sequence [i] based on digital (15, 97)-sequence over F16, using
(87−71, 87, 823)-Net in Base 16 — Upper bound on s
There is no (16, 87, 824)-net in base 16, because
- 1 times m-reduction [i] would yield (16, 86, 824)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 36 054060 013066 880239 818631 717185 914377 624602 653063 096545 650698 063775 707012 533771 310420 377483 194616 013851 > 1686 [i]