Best Known (54, 54+71, s)-Nets in Base 9
(54, 54+71, 98)-Net over F9 — Constructive and digital
Digital (54, 125, 98)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 41, 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 (13, 84, 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 (6, 41, 34)-net over F9, using
(54, 54+71, 182)-Net over F9 — Digital
Digital (54, 125, 182)-net over F9, using
- t-expansion [i] based on digital (50, 125, 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
(54, 54+71, 4156)-Net in Base 9 — Upper bound on s
There is no (54, 125, 4157)-net in base 9, because
- 1 times m-reduction [i] would yield (54, 124, 4157)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 21333 366096 582336 384794 194915 189504 999140 314832 311499 390129 302983 881728 302547 341566 965906 001542 169143 647027 619475 334905 > 9124 [i]