Best Known (149−77, 149, s)-Nets in Base 9
(149−77, 149, 165)-Net over F9 — Constructive and digital
Digital (72, 149, 165)-net over F9, using
- t-expansion [i] based on digital (64, 149, 165)-net over F9, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- net from sequence [i] based on digital (64, 164)-sequence over F9, using
(149−77, 149, 239)-Net over F9 — Digital
Digital (72, 149, 239)-net over F9, using
(149−77, 149, 9754)-Net in Base 9 — Upper bound on s
There is no (72, 149, 9755)-net in base 9, because
- 1 times m-reduction [i] would yield (72, 148, 9755)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 1693 537484 830103 392114 921876 781485 776874 979564 588470 743823 780147 699015 357683 279269 624355 095628 817932 360172 358421 754449 333538 152479 440250 380689 > 9148 [i]