Best Known (138−100, 138, s)-Nets in Base 9
(138−100, 138, 81)-Net over F9 — Constructive and digital
Digital (38, 138, 81)-net over F9, using
- t-expansion [i] based on digital (32, 138, 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
(138−100, 138, 128)-Net over F9 — Digital
Digital (38, 138, 128)-net over F9, using
- t-expansion [i] based on digital (33, 138, 128)-net over F9, using
- net from sequence [i] based on digital (33, 127)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 33 and N(F) ≥ 128, using
- net from sequence [i] based on digital (33, 127)-sequence over F9, using
(138−100, 138, 1017)-Net in Base 9 — Upper bound on s
There is no (38, 138, 1018)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 500757 703258 860280 054792 999080 563060 749332 389772 162294 318356 209404 083345 520278 880299 936837 634697 441735 088557 566348 290722 387366 406241 > 9138 [i]