Best Known (123−70, 123, s)-Nets in Base 9
(123−70, 123, 96)-Net over F9 — Constructive and digital
Digital (53, 123, 96)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 40, 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 (13, 83, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (5, 40, 32)-net over F9, using
(123−70, 123, 182)-Net over F9 — Digital
Digital (53, 123, 182)-net over F9, using
- t-expansion [i] based on digital (50, 123, 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
(123−70, 123, 3901)-Net in Base 9 — Upper bound on s
There is no (53, 123, 3902)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 2354 387318 143446 938687 481275 221170 802144 709692 915427 382169 750255 041010 637915 905500 948699 679348 996870 541511 177642 186897 > 9123 [i]