Best Known (51, 51+23, s)-Nets in Base 25
(51, 51+23, 1422)-Net over F25 — Constructive and digital
Digital (51, 74, 1422)-net over F25, using
- 253 times duplication [i] based on digital (48, 71, 1422)-net over F25, using
- net defined by OOA [i] based on linear OOA(2571, 1422, F25, 23, 23) (dual of [(1422, 23), 32635, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2571, 15643, F25, 23) (dual of [15643, 15572, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2571, 15644, F25, 23) (dual of [15644, 15573, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(2567, 15625, F25, 23) (dual of [15625, 15558, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2552, 15625, F25, 18) (dual of [15625, 15573, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(254, 19, F25, 4) (dual of [19, 15, 5]-code or 19-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(22) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(2571, 15644, F25, 23) (dual of [15644, 15573, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2571, 15643, F25, 23) (dual of [15643, 15572, 24]-code), using
- net defined by OOA [i] based on linear OOA(2571, 1422, F25, 23, 23) (dual of [(1422, 23), 32635, 24]-NRT-code), using
(51, 51+23, 19013)-Net over F25 — Digital
Digital (51, 74, 19013)-net over F25, using
(51, 51+23, large)-Net in Base 25 — Upper bound on s
There is no (51, 74, large)-net in base 25, because
- 21 times m-reduction [i] would yield (51, 53, large)-net in base 25, but