Best Known (58−45, 58, s)-Nets in Base 9
(58−45, 58, 64)-Net over F9 — Constructive and digital
Digital (13, 58, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
(58−45, 58, 322)-Net in Base 9 — Upper bound on s
There is no (13, 58, 323)-net in base 9, because
- 1 times m-reduction [i] would yield (13, 57, 323)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 2 508422 176815 013016 436689 640881 516126 371243 703123 181713 > 957 [i]