Best Known (59−43, 59, s)-Nets in Base 8
(59−43, 59, 65)-Net over F8 — Constructive and digital
Digital (16, 59, 65)-net over F8, using
- t-expansion [i] based on digital (14, 59, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
(59−43, 59, 374)-Net in Base 8 — Upper bound on s
There is no (16, 59, 375)-net in base 8, because
- 1 times m-reduction [i] would yield (16, 58, 375)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 25178 750838 488213 276940 350624 471506 747355 492801 412726 > 858 [i]