Best Known (46−14, 46, s)-Nets in Base 25
(46−14, 46, 2235)-Net over F25 — Constructive and digital
Digital (32, 46, 2235)-net over F25, using
- 251 times duplication [i] based on digital (31, 45, 2235)-net over F25, using
- net defined by OOA [i] based on linear OOA(2545, 2235, F25, 14, 14) (dual of [(2235, 14), 31245, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2545, 15645, F25, 14) (dual of [15645, 15600, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2545, 15648, F25, 14) (dual of [15648, 15603, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(7) [i] based on
- linear OA(2540, 15625, F25, 14) (dual of [15625, 15585, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2522, 15625, F25, 8) (dual of [15625, 15603, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(255, 23, F25, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- Reed–Solomon code RS(20,25) [i]
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- construction X applied to Ce(13) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(2545, 15648, F25, 14) (dual of [15648, 15603, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2545, 15645, F25, 14) (dual of [15645, 15600, 15]-code), using
- net defined by OOA [i] based on linear OOA(2545, 2235, F25, 14, 14) (dual of [(2235, 14), 31245, 15]-NRT-code), using
(46−14, 46, 20887)-Net over F25 — Digital
Digital (32, 46, 20887)-net over F25, using
(46−14, 46, large)-Net in Base 25 — Upper bound on s
There is no (32, 46, large)-net in base 25, because
- 12 times m-reduction [i] would yield (32, 34, large)-net in base 25, but