Best Known (58−33, 58, s)-Nets in Base 4
(58−33, 58, 34)-Net over F4 — Constructive and digital
Digital (25, 58, 34)-net over F4, using
- t-expansion [i] based on digital (21, 58, 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
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
(58−33, 58, 35)-Net in Base 4 — Constructive
(25, 58, 35)-net in base 4, using
- t-expansion [i] based on (24, 58, 35)-net in base 4, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
(58−33, 58, 51)-Net over F4 — Digital
Digital (25, 58, 51)-net over F4, using
- net from sequence [i] based on digital (25, 50)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 25 and N(F) ≥ 51, using
(58−33, 58, 303)-Net in Base 4 — Upper bound on s
There is no (25, 58, 304)-net in base 4, because
- 1 times m-reduction [i] would yield (25, 57, 304)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 21002 477232 488344 862631 803687 014042 > 457 [i]