Best Known (58, 58+91, s)-Nets in Base 8
(58, 58+91, 98)-Net over F8 — Constructive and digital
Digital (58, 149, 98)-net over F8, using
- t-expansion [i] based on digital (37, 149, 98)-net over F8, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 98, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
(58, 58+91, 144)-Net over F8 — Digital
Digital (58, 149, 144)-net over F8, using
- t-expansion [i] based on digital (45, 149, 144)-net over F8, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 45 and N(F) ≥ 144, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
(58, 58+91, 2322)-Net in Base 8 — Upper bound on s
There is no (58, 149, 2323)-net in base 8, because
- 1 times m-reduction [i] would yield (58, 148, 2323)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 45 778917 949140 407923 083101 958295 930086 226891 018386 147243 595642 000634 164548 436691 349254 472878 101521 209044 075704 775158 346376 412118 969792 > 8148 [i]