Best Known (59−35, 59, s)-Nets in Base 4
(59−35, 59, 34)-Net over F4 — Constructive and digital
Digital (24, 59, 34)-net over F4, using
- t-expansion [i] based on digital (21, 59, 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
(59−35, 59, 35)-Net in Base 4 — Constructive
(24, 59, 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
(59−35, 59, 49)-Net over F4 — Digital
Digital (24, 59, 49)-net over F4, using
- net from sequence [i] based on digital (24, 48)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 24 and N(F) ≥ 49, using
(59−35, 59, 257)-Net in Base 4 — Upper bound on s
There is no (24, 59, 258)-net in base 4, because
- 1 times m-reduction [i] would yield (24, 58, 258)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 85414 431481 154368 691609 378722 770064 > 458 [i]