Best Known (66, 66+76, s)-Nets in Base 9
(66, 66+76, 165)-Net over F9 — Constructive and digital
Digital (66, 142, 165)-net over F9, using
- t-expansion [i] based on digital (64, 142, 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+76, 199)-Net over F9 — Digital
Digital (66, 142, 199)-net over F9, using
(66, 66+76, 6888)-Net in Base 9 — Upper bound on s
There is no (66, 142, 6889)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 3194 352270 908619 984611 131072 973685 420602 614987 202586 972307 109178 576990 348442 498367 039758 602201 255968 243066 186525 211407 546855 126397 066609 > 9142 [i]