Best Known (59−14, 59, s)-Nets in Base 25
(59−14, 59, 55807)-Net over F25 — Constructive and digital
Digital (45, 59, 55807)-net over F25, using
- 252 times duplication [i] based on digital (43, 57, 55807)-net over F25, using
- net defined by OOA [i] based on linear OOA(2557, 55807, F25, 14, 14) (dual of [(55807, 14), 781241, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2557, 390649, F25, 14) (dual of [390649, 390592, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
- linear OA(2553, 390625, F25, 14) (dual of [390625, 390572, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2533, 390625, F25, 9) (dual of [390625, 390592, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(13) ⊂ Ce(8) [i] based on
- OA 7-folding and stacking [i] based on linear OA(2557, 390649, F25, 14) (dual of [390649, 390592, 15]-code), using
- net defined by OOA [i] based on linear OOA(2557, 55807, F25, 14, 14) (dual of [(55807, 14), 781241, 15]-NRT-code), using
(59−14, 59, 522032)-Net over F25 — Digital
Digital (45, 59, 522032)-net over F25, using
(59−14, 59, large)-Net in Base 25 — Upper bound on s
There is no (45, 59, large)-net in base 25, because
- 12 times m-reduction [i] would yield (45, 47, large)-net in base 25, but