Best Known (33, 33+30, s)-Nets in Base 25
(33, 33+30, 208)-Net over F25 — Constructive and digital
Digital (33, 63, 208)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (9, 24, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- digital (9, 39, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25 (see above)
- digital (9, 24, 104)-net over F25, using
(33, 33+30, 574)-Net over F25 — Digital
Digital (33, 63, 574)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2563, 574, F25, 30) (dual of [574, 511, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2563, 645, F25, 30) (dual of [645, 582, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(21) [i] based on
- linear OA(2556, 625, F25, 30) (dual of [625, 569, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2543, 625, F25, 22) (dual of [625, 582, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(257, 20, F25, 7) (dual of [20, 13, 8]-code or 20-arc in PG(6,25)), using
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), using
- Reed–Solomon code RS(18,25) [i]
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), using
- construction X applied to Ce(29) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(2563, 645, F25, 30) (dual of [645, 582, 31]-code), using
(33, 33+30, 199015)-Net in Base 25 — Upper bound on s
There is no (33, 63, 199016)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 11755 429329 129334 859855 031661 635968 340399 690008 032486 871022 541900 268417 718554 616937 328449 > 2563 [i]