Best Known (42, 42+83, s)-Nets in Base 9
(42, 42+83, 81)-Net over F9 — Constructive and digital
Digital (42, 125, 81)-net over F9, using
- t-expansion [i] based on digital (32, 125, 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
(42, 42+83, 140)-Net over F9 — Digital
Digital (42, 125, 140)-net over F9, using
- t-expansion [i] based on digital (39, 125, 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
(42, 42+83, 1526)-Net in Base 9 — Upper bound on s
There is no (42, 125, 1527)-net in base 9, because
- 1 times m-reduction [i] would yield (42, 124, 1527)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 21325 241673 208644 930519 544331 045328 852621 430770 002838 380568 476519 424551 565180 137873 500446 581872 633460 525547 231244 523641 > 9124 [i]