Best Known (64, 64+67, s)-Nets in Base 9
(64, 64+67, 165)-Net over F9 — Constructive and digital
Digital (64, 131, 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
(64, 64+67, 224)-Net over F9 — Digital
Digital (64, 131, 224)-net over F9, using
(64, 64+67, 9429)-Net in Base 9 — Upper bound on s
There is no (64, 131, 9430)-net in base 9, because
- 1 times m-reduction [i] would yield (64, 130, 9430)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 11290 260478 998058 081796 956114 960709 121459 576189 273766 735150 846098 231478 988335 774647 690903 108473 790291 275003 276942 863114 170545 > 9130 [i]