Best Known (52−31, 52, s)-Nets in Base 4
(52−31, 52, 34)-Net over F4 — Constructive and digital
Digital (21, 52, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second 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) = 21 and N(F) ≥ 34, using
(52−31, 52, 44)-Net over F4 — Digital
Digital (21, 52, 44)-net over F4, using
- net from sequence [i] based on digital (21, 43)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 44, using
(52−31, 52, 226)-Net in Base 4 — Upper bound on s
There is no (21, 52, 227)-net in base 4, because
- 1 times m-reduction [i] would yield (21, 51, 227)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 5 129161 848239 441608 121039 559424 > 451 [i]