Best Known (139−106, 139, s)-Nets in Base 9
(139−106, 139, 81)-Net over F9 — Constructive and digital
Digital (33, 139, 81)-net over F9, using
- t-expansion [i] based on digital (32, 139, 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
(139−106, 139, 128)-Net over F9 — Digital
Digital (33, 139, 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
(139−106, 139, 786)-Net in Base 9 — Upper bound on s
There is no (33, 139, 787)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 4 405155 303821 241756 616605 164781 760682 154092 529984 713564 534602 013610 199644 066720 881705 725375 618325 584838 151523 745282 972632 331210 653305 > 9139 [i]