Best Known (37−25, 37, s)-Nets in Base 9
(37−25, 37, 40)-Net over F9 — Constructive and digital
Digital (12, 37, 40)-net over F9, using
- t-expansion [i] based on digital (8, 37, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
(37−25, 37, 56)-Net over F9 — Digital
Digital (12, 37, 56)-net over F9, using
- net from sequence [i] based on digital (12, 55)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 12 and N(F) ≥ 56, using
(37−25, 37, 474)-Net in Base 9 — Upper bound on s
There is no (12, 37, 475)-net in base 9, because
- 1 times m-reduction [i] would yield (12, 36, 475)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 22540 691094 471679 988755 842194 448161 > 936 [i]