Best Known (124−75, 124, s)-Nets in Base 9
(124−75, 124, 81)-Net over F9 — Constructive and digital
Digital (49, 124, 81)-net over F9, using
- t-expansion [i] based on digital (32, 124, 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
(124−75, 124, 82)-Net in Base 9 — Constructive
(49, 124, 82)-net in base 9, using
- 2 times m-reduction [i] based on (49, 126, 82)-net in base 9, using
- base change [i] based on digital (7, 84, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- base change [i] based on digital (7, 84, 82)-net over F27, using
(124−75, 124, 168)-Net over F9 — Digital
Digital (49, 124, 168)-net over F9, using
- net from sequence [i] based on digital (49, 167)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 49 and N(F) ≥ 168, using
(124−75, 124, 2700)-Net in Base 9 — Upper bound on s
There is no (49, 124, 2701)-net in base 9, because
- 1 times m-reduction [i] would yield (49, 123, 2701)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 2375 296931 575688 100513 558867 988075 857764 933535 552171 069731 532150 379419 789691 552420 969889 799566 056814 632106 322713 407113 > 9123 [i]