Best Known (121−66, 121, s)-Nets in Base 9
(121−66, 121, 106)-Net over F9 — Constructive and digital
Digital (55, 121, 106)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 38, 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, 83, 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, 38, 32)-net over F9, using
(121−66, 121, 182)-Net over F9 — Digital
Digital (55, 121, 182)-net over F9, using
- t-expansion [i] based on digital (50, 121, 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
(121−66, 121, 5169)-Net in Base 9 — Upper bound on s
There is no (55, 121, 5170)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 29 113092 453358 033476 424175 666749 439156 360255 178376 228926 414769 748012 125104 105370 514282 345485 600949 650557 570016 100241 > 9121 [i]