Best Known (43, 63, s)-Nets in Base 25
(43, 63, 1564)-Net over F25 — Constructive and digital
Digital (43, 63, 1564)-net over F25, using
- 1 times m-reduction [i] based on digital (43, 64, 1564)-net over F25, using
- net defined by OOA [i] based on linear OOA(2564, 1564, F25, 21, 21) (dual of [(1564, 21), 32780, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2564, 15641, F25, 21) (dual of [15641, 15577, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- 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(2549, 15626, F25, 17) (dual of [15626, 15577, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(253, 15, F25, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,25) or 15-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- OOA 10-folding and stacking with additional row [i] based on linear OA(2564, 15641, F25, 21) (dual of [15641, 15577, 22]-code), using
- net defined by OOA [i] based on linear OOA(2564, 1564, F25, 21, 21) (dual of [(1564, 21), 32780, 22]-NRT-code), using
(43, 63, 15648)-Net over F25 — Digital
Digital (43, 63, 15648)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2563, 15648, F25, 20) (dual of [15648, 15585, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- 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(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(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(19) ⊂ Ce(13) [i] based on
(43, 63, large)-Net in Base 25 — Upper bound on s
There is no (43, 63, large)-net in base 25, because
- 18 times m-reduction [i] would yield (43, 45, large)-net in base 25, but