Best Known (70−35, 70, s)-Nets in Base 4
(70−35, 70, 56)-Net over F4 — Constructive and digital
Digital (35, 70, 56)-net over F4, using
- t-expansion [i] based on digital (33, 70, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
(70−35, 70, 65)-Net over F4 — Digital
Digital (35, 70, 65)-net over F4, using
- t-expansion [i] based on digital (33, 70, 65)-net over F4, using
- net from sequence [i] based on digital (33, 64)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 65, using
- net from sequence [i] based on digital (33, 64)-sequence over F4, using
(70−35, 70, 650)-Net in Base 4 — Upper bound on s
There is no (35, 70, 651)-net in base 4, because
- 1 times m-reduction [i] would yield (35, 69, 651)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 349189 009624 925557 128972 393018 473556 386704 > 469 [i]