Best Known (31, 73, s)-Nets in Base 25
(31, 73, 204)-Net over F25 — Constructive and digital
Digital (31, 73, 204)-net over F25, using
- t-expansion [i] based on digital (30, 73, 204)-net over F25, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 30 and N(F) ≥ 204, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
(31, 73, 205)-Net over F25 — Digital
Digital (31, 73, 205)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2573, 205, F25, 2, 42) (dual of [(205, 2), 337, 43]-NRT-code), using
- construction X applied to AG(2;F,355P) ⊂ AG(2;F,362P) [i] based on
- linear OOA(2567, 199, F25, 2, 42) (dual of [(199, 2), 331, 43]-NRT-code), using algebraic-geometric NRT-code AG(2;F,355P) [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- linear OOA(2560, 199, F25, 2, 35) (dual of [(199, 2), 338, 36]-NRT-code), using algebraic-geometric NRT-code AG(2;F,362P) [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200 (see above)
- linear OOA(256, 6, F25, 2, 6) (dual of [(6, 2), 6, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(256, 25, F25, 2, 6) (dual of [(25, 2), 44, 7]-NRT-code), using
- Reed–Solomon NRT-code RS(2;44,25) [i]
- discarding factors / shortening the dual code based on linear OOA(256, 25, F25, 2, 6) (dual of [(25, 2), 44, 7]-NRT-code), using
- construction X applied to AG(2;F,355P) ⊂ AG(2;F,362P) [i] based on
(31, 73, 26158)-Net in Base 25 — Upper bound on s
There is no (31, 73, 26159)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 1 121828 352569 070333 575967 429109 413259 954385 204598 599167 837978 523924 422393 959897 481665 120299 819913 248905 > 2573 [i]