Best Known (125−69, 125, s)-Nets in Base 9
(125−69, 125, 106)-Net over F9 — Constructive and digital
Digital (56, 125, 106)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 39, 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, 86, 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, 39, 32)-net over F9, using
(125−69, 125, 182)-Net over F9 — Digital
Digital (56, 125, 182)-net over F9, using
- t-expansion [i] based on digital (50, 125, 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
(125−69, 125, 5090)-Net in Base 9 — Upper bound on s
There is no (56, 125, 5091)-net in base 9, because
- 1 times m-reduction [i] would yield (56, 124, 5091)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 21192 875420 508005 982589 973675 269213 095052 210786 965463 548296 969798 998866 143463 815019 347644 420363 176875 570970 600815 857329 > 9124 [i]