Best Known (99−58, 99, s)-Nets in Base 9
(99−58, 99, 81)-Net over F9 — Constructive and digital
Digital (41, 99, 81)-net over F9, using
- t-expansion [i] based on digital (32, 99, 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
(99−58, 99, 84)-Net in Base 9 — Constructive
(41, 99, 84)-net in base 9, using
- base change [i] based on digital (8, 66, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
(99−58, 99, 140)-Net over F9 — Digital
Digital (41, 99, 140)-net over F9, using
- t-expansion [i] based on digital (39, 99, 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
(99−58, 99, 2622)-Net in Base 9 — Upper bound on s
There is no (41, 99, 2623)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 29675 639283 862151 902162 720310 283835 102736 770437 969335 170192 905883 714379 609109 247965 812330 567961 > 999 [i]