Best Known (61, 61+32, s)-Nets in Base 25
(61, 61+32, 977)-Net over F25 — Constructive and digital
Digital (61, 93, 977)-net over F25, using
- 251 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
(61, 61+32, 9703)-Net over F25 — Digital
Digital (61, 93, 9703)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2593, 9703, F25, 32) (dual of [9703, 9610, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2593, 15636, F25, 32) (dual of [15636, 15543, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(28) [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(2582, 15625, F25, 29) (dual of [15625, 15543, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(31) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(2593, 15636, F25, 32) (dual of [15636, 15543, 33]-code), using
(61, 61+32, large)-Net in Base 25 — Upper bound on s
There is no (61, 93, large)-net in base 25, because
- 30 times m-reduction [i] would yield (61, 63, large)-net in base 25, but