Best Known (64, 64+63, s)-Nets in Base 9
(64, 64+63, 165)-Net over F9 — Constructive and digital
Digital (64, 127, 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+63, 249)-Net over F9 — Digital
Digital (64, 127, 249)-net over F9, using
(64, 64+63, 11715)-Net in Base 9 — Upper bound on s
There is no (64, 127, 11716)-net in base 9, because
- 1 times m-reduction [i] would yield (64, 126, 11716)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 1 716287 479461 108362 646762 949696 124268 117655 362806 993352 563420 576716 625572 669974 035629 065888 163937 722458 302140 611191 005281 > 9126 [i]