Best Known (138−76, 138, s)-Nets in Base 9
(138−76, 138, 110)-Net over F9 — Constructive and digital
Digital (62, 138, 110)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (7, 45, 36)-net over F9, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 36, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- digital (17, 93, 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 (7, 45, 36)-net over F9, using
(138−76, 138, 192)-Net over F9 — Digital
Digital (62, 138, 192)-net over F9, using
- t-expansion [i] based on digital (61, 138, 192)-net over F9, using
- net from sequence [i] based on digital (61, 191)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 61 and N(F) ≥ 192, using
- net from sequence [i] based on digital (61, 191)-sequence over F9, using
(138−76, 138, 5461)-Net in Base 9 — Upper bound on s
There is no (62, 138, 5462)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 487838 612986 334689 251119 082971 172817 180130 898778 709351 450711 747763 686762 347191 020843 448795 765284 276713 110657 927507 625603 411307 208417 > 9138 [i]