Best Known (125−84, 125, s)-Nets in Base 9
(125−84, 125, 81)-Net over F9 — Constructive and digital
Digital (41, 125, 81)-net over F9, using
- t-expansion [i] based on digital (32, 125, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(125−84, 125, 140)-Net over F9 — Digital
Digital (41, 125, 140)-net over F9, using
- t-expansion [i] based on digital (39, 125, 140)-net over F9, using
- net from sequence [i] based on digital (39, 139)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 39 and N(F) ≥ 140, using
- net from sequence [i] based on digital (39, 139)-sequence over F9, using
(125−84, 125, 1402)-Net in Base 9 — Upper bound on s
There is no (41, 125, 1403)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 194328 881168 006983 578290 776201 821942 638197 234491 983069 649320 796942 755443 316616 596645 401278 824599 143001 671542 208997 845489 > 9125 [i]