Best Known (74−36, 74, s)-Nets in Base 25
(74−36, 74, 252)-Net over F25 — Constructive and digital
Digital (38, 74, 252)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (10, 28, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- digital (10, 46, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25 (see above)
- digital (10, 28, 126)-net over F25, using
(74−36, 74, 550)-Net over F25 — Digital
Digital (38, 74, 550)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2574, 550, F25, 36) (dual of [550, 476, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(2574, 645, F25, 36) (dual of [645, 571, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(28) [i] based on
- linear OA(2568, 625, F25, 36) (dual of [625, 557, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2554, 625, F25, 29) (dual of [625, 571, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(256, 20, F25, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,25)), using
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using
- Reed–Solomon code RS(19,25) [i]
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using
- construction X applied to Ce(35) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(2574, 645, F25, 36) (dual of [645, 571, 37]-code), using
(74−36, 74, 175785)-Net in Base 25 — Upper bound on s
There is no (38, 74, 175786)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 28 027849 549658 756482 122319 270939 704200 589970 675629 926260 863512 703726 989265 666328 102446 007402 180996 389025 > 2574 [i]