Best Known (41, 41+20, s)-Nets in Base 25
(41, 41+20, 1564)-Net over F25 — Constructive and digital
Digital (41, 61, 1564)-net over F25, using
- net defined by OOA [i] based on linear OOA(2561, 1564, F25, 20, 20) (dual of [(1564, 20), 31219, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2561, 15640, F25, 20) (dual of [15640, 15579, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [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(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(19) ⊂ Ce(15) [i] based on
- OA 10-folding and stacking [i] based on linear OA(2561, 15640, F25, 20) (dual of [15640, 15579, 21]-code), using
(41, 41+20, 14370)-Net over F25 — Digital
Digital (41, 61, 14370)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2561, 14370, F25, 20) (dual of [14370, 14309, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, 15640, F25, 20) (dual of [15640, 15579, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [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(2546, 15625, F25, 16) (dual of [15625, 15579, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(19) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(2561, 15640, F25, 20) (dual of [15640, 15579, 21]-code), using
(41, 41+20, large)-Net in Base 25 — Upper bound on s
There is no (41, 61, large)-net in base 25, because
- 18 times m-reduction [i] would yield (41, 43, large)-net in base 25, but