Best Known (64−29, 64, s)-Nets in Base 7
(64−29, 64, 106)-Net over F7 — Constructive and digital
Digital (35, 64, 106)-net over F7, using
- trace code for nets [i] based on digital (3, 32, 53)-net over F49, using
- net from sequence [i] based on digital (3, 52)-sequence over F49, using
(64−29, 64, 184)-Net over F7 — Digital
Digital (35, 64, 184)-net over F7, using
- trace code for nets [i] based on digital (3, 32, 92)-net over F49, using
- net from sequence [i] based on digital (3, 91)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
- net from sequence [i] based on digital (3, 91)-sequence over F49, using
(64−29, 64, 6392)-Net in Base 7 — Upper bound on s
There is no (35, 64, 6393)-net in base 7, because
- 1 times m-reduction [i] would yield (35, 63, 6393)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 174568 714249 086636 206301 566613 661466 692014 484923 743041 > 763 [i]