Best Known (46, 69, s)-Nets in Base 25
(46, 69, 1421)-Net over F25 — Constructive and digital
Digital (46, 69, 1421)-net over F25, using
- 251 times duplication [i] based on digital (45, 68, 1421)-net over F25, using
- net defined by OOA [i] based on linear OOA(2568, 1421, F25, 23, 23) (dual of [(1421, 23), 32615, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2568, 15632, F25, 23) (dual of [15632, 15564, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2568, 15633, F25, 23) (dual of [15633, 15565, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(2567, 15626, F25, 23) (dual of [15626, 15559, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(2561, 15626, F25, 21) (dual of [15626, 15565, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(251, 7, F25, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2568, 15633, F25, 23) (dual of [15633, 15565, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2568, 15632, F25, 23) (dual of [15632, 15564, 24]-code), using
- net defined by OOA [i] based on linear OOA(2568, 1421, F25, 23, 23) (dual of [(1421, 23), 32615, 24]-NRT-code), using
(46, 69, 12150)-Net over F25 — Digital
Digital (46, 69, 12150)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2569, 12150, F25, 23) (dual of [12150, 12081, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2569, 15636, F25, 23) (dual of [15636, 15567, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [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(2558, 15625, F25, 20) (dual of [15625, 15567, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(252, 11, F25, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(2569, 15636, F25, 23) (dual of [15636, 15567, 24]-code), using
(46, 69, large)-Net in Base 25 — Upper bound on s
There is no (46, 69, large)-net in base 25, because
- 21 times m-reduction [i] would yield (46, 48, large)-net in base 25, but