Best Known (66, 66+72, s)-Nets in Base 9
(66, 66+72, 165)-Net over F9 — Constructive and digital
Digital (66, 138, 165)-net over F9, using
- t-expansion [i] based on digital (64, 138, 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
(66, 66+72, 215)-Net over F9 — Digital
Digital (66, 138, 215)-net over F9, using
(66, 66+72, 8098)-Net in Base 9 — Upper bound on s
There is no (66, 138, 8099)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 485973 963927 010501 369199 966723 057541 556743 857211 840104 539150 869521 349172 801239 956229 115584 124657 752638 497153 001622 275531 437835 538529 > 9138 [i]