Best Known (31, 41, s)-Nets in Base 25
(31, 41, 78129)-Net over F25 — Constructive and digital
Digital (31, 41, 78129)-net over F25, using
- net defined by OOA [i] based on linear OOA(2541, 78129, F25, 10, 10) (dual of [(78129, 10), 781249, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2541, 390645, F25, 10) (dual of [390645, 390604, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2541, 390649, F25, 10) (dual of [390649, 390608, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(4) [i] based on
- linear OA(2537, 390625, F25, 10) (dual of [390625, 390588, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2517, 390625, F25, 5) (dual of [390625, 390608, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(254, 24, F25, 4) (dual of [24, 20, 5]-code or 24-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(9) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(2541, 390649, F25, 10) (dual of [390649, 390608, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2541, 390645, F25, 10) (dual of [390645, 390604, 11]-code), using
(31, 41, 403588)-Net over F25 — Digital
Digital (31, 41, 403588)-net over F25, using
(31, 41, large)-Net in Base 25 — Upper bound on s
There is no (31, 41, large)-net in base 25, because
- 8 times m-reduction [i] would yield (31, 33, large)-net in base 25, but