Best Known (47−22, 47, s)-Nets in Base 25
(47−22, 47, 200)-Net over F25 — Constructive and digital
Digital (25, 47, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
(47−22, 47, 559)-Net over F25 — Digital
Digital (25, 47, 559)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2547, 559, F25, 22) (dual of [559, 512, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2547, 639, F25, 22) (dual of [639, 592, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- 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(2533, 625, F25, 17) (dual of [625, 592, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(254, 14, F25, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(2547, 639, F25, 22) (dual of [639, 592, 23]-code), using
(47−22, 47, 192223)-Net in Base 25 — Upper bound on s
There is no (25, 47, 192224)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 504878 996385 528066 390619 098314 130989 399170 358847 049524 487795 243777 > 2547 [i]