Best Known (70, 70+76, s)-Nets in Base 9
(70, 70+76, 165)-Net over F9 — Constructive and digital
Digital (70, 146, 165)-net over F9, using
- t-expansion [i] based on digital (64, 146, 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
(70, 70+76, 228)-Net over F9 — Digital
Digital (70, 146, 228)-net over F9, using
(70, 70+76, 8686)-Net in Base 9 — Upper bound on s
There is no (70, 146, 8687)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 20 894311 184853 173630 081803 879153 896877 752088 234996 834475 701312 949869 575594 626469 473713 668377 169468 080595 090971 559740 287690 098263 167550 024145 > 9146 [i]