Best Known (59, 134, s)-Nets in Base 9
(59, 134, 106)-Net over F9 — Constructive and digital
Digital (59, 134, 106)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 42, 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, 92, 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, 42, 32)-net over F9, using
(59, 134, 182)-Net over F9 — Digital
Digital (59, 134, 182)-net over F9, using
- t-expansion [i] based on digital (50, 134, 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
(59, 134, 4908)-Net in Base 9 — Upper bound on s
There is no (59, 134, 4909)-net in base 9, because
- 1 times m-reduction [i] would yield (59, 133, 4909)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 8 243753 004367 917395 989662 090090 099448 119680 494123 288118 058481 489759 468963 845959 184768 340873 701087 863110 002002 714024 654480 605065 > 9133 [i]