Best Known (68, 68+79, s)-Nets in Base 9
(68, 68+79, 165)-Net over F9 — Constructive and digital
Digital (68, 147, 165)-net over F9, using
- t-expansion [i] based on digital (64, 147, 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+79, 201)-Net over F9 — Digital
Digital (68, 147, 201)-net over F9, using
(68, 68+79, 7164)-Net in Base 9 — Upper bound on s
There is no (68, 147, 7165)-net in base 9, because
- 1 times m-reduction [i] would yield (68, 146, 7165)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 20 924058 969717 328880 158202 301481 609177 653505 720036 789360 238197 103282 327765 128768 878805 684019 956262 012069 646756 006173 141137 120201 137423 213081 > 9146 [i]