Best Known (58, 58+73, s)-Nets in Base 9
(58, 58+73, 106)-Net over F9 — Constructive and digital
Digital (58, 131, 106)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 41, 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 (17, 90, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- digital (5, 41, 32)-net over F9, using
(58, 58+73, 182)-Net over F9 — Digital
Digital (58, 131, 182)-net over F9, using
- t-expansion [i] based on digital (50, 131, 182)-net over F9, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 50 and N(F) ≥ 182, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
(58, 58+73, 4961)-Net in Base 9 — Upper bound on s
There is no (58, 131, 4962)-net in base 9, because
- 1 times m-reduction [i] would yield (58, 130, 4962)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 11308 995416 163958 795696 565504 112077 954677 023651 374536 923931 855691 202129 496749 726112 331873 549475 543055 531302 770202 967259 348673 > 9130 [i]