Best Known (145−85, 145, s)-Nets in Base 9
(145−85, 145, 96)-Net over F9 — Constructive and digital
Digital (60, 145, 96)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 47, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- digital (13, 98, 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
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (5, 47, 32)-net over F9, using
(145−85, 145, 190)-Net over F9 — Digital
Digital (60, 145, 190)-net over F9, using
- net from sequence [i] based on digital (60, 189)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 60 and N(F) ≥ 190, using
(145−85, 145, 3832)-Net in Base 9 — Upper bound on s
There is no (60, 145, 3833)-net in base 9, because
- 1 times m-reduction [i] would yield (60, 144, 3833)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 258596 442324 899917 402385 332233 629501 574484 367900 423098 014194 896703 868728 608556 229637 504727 538056 846178 001587 446948 774203 687894 514765 152017 > 9144 [i]