Best Known (52, 52+56, s)-Nets in Base 9
(52, 52+56, 110)-Net over F9 — Constructive and digital
Digital (52, 108, 110)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (7, 35, 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, 73, 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, 35, 36)-net over F9, using
(52, 52+56, 182)-Net over F9 — Digital
Digital (52, 108, 182)-net over F9, using
- t-expansion [i] based on digital (50, 108, 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
(52, 52+56, 6752)-Net in Base 9 — Upper bound on s
There is no (52, 108, 6753)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 11 450878 323127 616053 543015 666101 148502 676321 695102 224296 144689 111083 779675 293243 043228 949208 688700 580705 > 9108 [i]