Best Known (68, 68+71, s)-Nets in Base 9
(68, 68+71, 165)-Net over F9 — Constructive and digital
Digital (68, 139, 165)-net over F9, using
- t-expansion [i] based on digital (64, 139, 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+71, 237)-Net over F9 — Digital
Digital (68, 139, 237)-net over F9, using
(68, 68+71, 10039)-Net in Base 9 — Upper bound on s
There is no (68, 139, 10040)-net in base 9, because
- 1 times m-reduction [i] would yield (68, 138, 10040)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 486299 084385 818945 705938 839225 047399 486115 791754 471998 877713 416437 085753 509820 753392 773316 881942 885487 257732 709034 413706 404971 147841 > 9138 [i]