Best Known (68, 68+76, s)-Nets in Base 9
(68, 68+76, 165)-Net over F9 — Constructive and digital
Digital (68, 144, 165)-net over F9, using
- t-expansion [i] based on digital (64, 144, 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
(68, 68+76, 213)-Net over F9 — Digital
Digital (68, 144, 213)-net over F9, using
(68, 68+76, 7735)-Net in Base 9 — Upper bound on s
There is no (68, 144, 7736)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 258229 476193 892666 080336 599867 637484 888437 233434 149963 321658 946993 849212 749390 555547 472218 615399 885699 006922 027179 051323 953048 114500 383617 > 9144 [i]