Best Known (62, 62+32, s)-Nets in Base 25
(62, 62+32, 977)-Net over F25 — Constructive and digital
Digital (62, 94, 977)-net over F25, using
- 252 times duplication [i] based on digital (60, 92, 977)-net over F25, using
- net defined by OOA [i] based on linear OOA(2592, 977, F25, 32, 32) (dual of [(977, 32), 31172, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(2592, 15632, F25, 32) (dual of [15632, 15540, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(29) [i] based on
- linear OA(2591, 15625, F25, 32) (dual of [15625, 15534, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2585, 15625, F25, 30) (dual of [15625, 15540, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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 Ce(31) ⊂ Ce(29) [i] based on
- OA 16-folding and stacking [i] based on linear OA(2592, 15632, F25, 32) (dual of [15632, 15540, 33]-code), using
- net defined by OOA [i] based on linear OOA(2592, 977, F25, 32, 32) (dual of [(977, 32), 31172, 33]-NRT-code), using
(62, 62+32, 10804)-Net over F25 — Digital
Digital (62, 94, 10804)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2594, 10804, F25, 32) (dual of [10804, 10710, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2594, 15640, F25, 32) (dual of [15640, 15546, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
- linear OA(2591, 15625, F25, 32) (dual of [15625, 15534, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2579, 15625, F25, 28) (dual of [15625, 15546, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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 Ce(31) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(2594, 15640, F25, 32) (dual of [15640, 15546, 33]-code), using
(62, 62+32, large)-Net in Base 25 — Upper bound on s
There is no (62, 94, large)-net in base 25, because
- 30 times m-reduction [i] would yield (62, 64, large)-net in base 25, but