Best Known (111−59, 111, s)-Nets in Base 9
(111−59, 111, 108)-Net over F9 — Constructive and digital
Digital (52, 111, 108)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 35, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- digital (17, 76, 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 (6, 35, 34)-net over F9, using
(111−59, 111, 182)-Net over F9 — Digital
Digital (52, 111, 182)-net over F9, using
- t-expansion [i] based on digital (50, 111, 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
(111−59, 111, 6057)-Net in Base 9 — Upper bound on s
There is no (52, 111, 6058)-net in base 9, because
- 1 times m-reduction [i] would yield (52, 110, 6058)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 927 208214 199737 413582 225234 178757 604121 338266 481217 538888 673670 218775 798321 627091 893529 568545 710787 246225 > 9110 [i]