Best Known (126−75, 126, s)-Nets in Base 9
(126−75, 126, 81)-Net over F9 — Constructive and digital
Digital (51, 126, 81)-net over F9, using
- t-expansion [i] based on digital (32, 126, 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
(126−75, 126, 88)-Net in Base 9 — Constructive
(51, 126, 88)-net in base 9, using
- base change [i] based on digital (9, 84, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
(126−75, 126, 182)-Net over F9 — Digital
Digital (51, 126, 182)-net over F9, using
- t-expansion [i] based on digital (50, 126, 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
(126−75, 126, 3043)-Net in Base 9 — Upper bound on s
There is no (51, 126, 3044)-net in base 9, because
- 1 times m-reduction [i] would yield (51, 125, 3044)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 191329 011661 821848 101927 570311 827796 675144 332781 266830 234828 068792 393291 905444 528394 463258 100336 616016 817819 617989 761185 > 9125 [i]