Best Known (66−22, 66, s)-Nets in Base 25
(66−22, 66, 1421)-Net over F25 — Constructive and digital
Digital (44, 66, 1421)-net over F25, using
- 251 times duplication [i] based on digital (43, 65, 1421)-net over F25, using
- net defined by OOA [i] based on linear OOA(2565, 1421, F25, 22, 22) (dual of [(1421, 22), 31197, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2565, 15631, F25, 22) (dual of [15631, 15566, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2565, 15632, F25, 22) (dual of [15632, 15567, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(2564, 15625, F25, 22) (dual of [15625, 15561, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(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(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(2565, 15632, F25, 22) (dual of [15632, 15567, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2565, 15631, F25, 22) (dual of [15631, 15566, 23]-code), using
- net defined by OOA [i] based on linear OOA(2565, 1421, F25, 22, 22) (dual of [(1421, 22), 31197, 23]-NRT-code), using
(66−22, 66, 12079)-Net over F25 — Digital
Digital (44, 66, 12079)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2566, 12079, F25, 22) (dual of [12079, 12013, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2566, 15636, F25, 22) (dual of [15636, 15570, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(2564, 15625, F25, 22) (dual of [15625, 15561, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2555, 15625, F25, 19) (dual of [15625, 15570, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(2566, 15636, F25, 22) (dual of [15636, 15570, 23]-code), using
(66−22, 66, large)-Net in Base 25 — Upper bound on s
There is no (44, 66, large)-net in base 25, because
- 20 times m-reduction [i] would yield (44, 46, large)-net in base 25, but