Best Known (131−72, 131, s)-Nets in Base 9
(131−72, 131, 108)-Net over F9 — Constructive and digital
Digital (59, 131, 108)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 42, 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, 89, 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, 42, 34)-net over F9, using
(131−72, 131, 182)-Net over F9 — Digital
Digital (59, 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
(131−72, 131, 5275)-Net in Base 9 — Upper bound on s
There is no (59, 131, 5276)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 102012 984415 736137 181007 388970 453730 802073 405023 669282 232071 782257 702568 400008 083403 771059 578148 708975 302247 955417 309888 006273 > 9131 [i]