Best Known (36, 69, s)-Nets in Base 4
(36, 69, 56)-Net over F4 — Constructive and digital
Digital (36, 69, 56)-net over F4, using
- t-expansion [i] based on digital (33, 69, 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
(36, 69, 70)-Net over F4 — Digital
Digital (36, 69, 70)-net over F4, using
(36, 69, 807)-Net in Base 4 — Upper bound on s
There is no (36, 69, 808)-net in base 4, because
- 1 times m-reduction [i] would yield (36, 68, 808)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 87246 028207 800955 563192 068036 896256 918350 > 468 [i]