Best Known (137−78, 137, s)-Nets in Base 9
(137−78, 137, 102)-Net over F9 — Constructive and digital
Digital (59, 137, 102)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 42, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- digital (17, 95, 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 (3, 42, 28)-net over F9, using
(137−78, 137, 182)-Net over F9 — Digital
Digital (59, 137, 182)-net over F9, using
- t-expansion [i] based on digital (50, 137, 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
(137−78, 137, 4305)-Net in Base 9 — Upper bound on s
There is no (59, 137, 4306)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 54114 341991 254278 192164 484780 354015 146550 437163 227787 918044 768254 205291 204257 770368 284026 215243 396728 492178 133594 558430 871486 528945 > 9137 [i]