Best Known (25, 25+58, s)-Nets in Base 4
(25, 25+58, 34)-Net over F4 — Constructive and digital
Digital (25, 83, 34)-net over F4, using
- t-expansion [i] based on digital (21, 83, 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
(25, 25+58, 35)-Net in Base 4 — Constructive
(25, 83, 35)-net in base 4, using
- t-expansion [i] based on (24, 83, 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
(25, 25+58, 51)-Net over F4 — Digital
Digital (25, 83, 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
(25, 25+58, 140)-Net in Base 4 — Upper bound on s
There is no (25, 83, 141)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(483, 141, S4, 58), but
- the linear programming bound shows that M ≥ 3021 825421 374945 162729 264431 504057 792160 958436 471970 277157 797065 975547 208948 779022 376336 510719 563664 112502 744331 170857 076856 085599 485952 / 30 413087 614600 062687 101050 096553 420686 920679 479441 406126 063885 691633 011395 926949 609375 > 483 [i]