Best Known (62, 62+33, s)-Nets in Base 25
(62, 62+33, 976)-Net over F25 — Constructive and digital
Digital (62, 95, 976)-net over F25, using
- 251 times duplication [i] based on digital (61, 94, 976)-net over F25, using
- net defined by OOA [i] based on linear OOA(2594, 976, F25, 33, 33) (dual of [(976, 33), 32114, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(2594, 15617, F25, 33) (dual of [15617, 15523, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2594, 15625, F25, 33) (dual of [15625, 15531, 34]-code), using
- an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- discarding factors / shortening the dual code based on linear OA(2594, 15625, F25, 33) (dual of [15625, 15531, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(2594, 15617, F25, 33) (dual of [15617, 15523, 34]-code), using
- net defined by OOA [i] based on linear OOA(2594, 976, F25, 33, 33) (dual of [(976, 33), 32114, 34]-NRT-code), using
(62, 62+33, 8953)-Net over F25 — Digital
Digital (62, 95, 8953)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2595, 8953, F25, 33) (dual of [8953, 8858, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2595, 15632, F25, 33) (dual of [15632, 15537, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- linear OA(2594, 15625, F25, 33) (dual of [15625, 15531, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2588, 15625, F25, 31) (dual of [15625, 15537, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(32) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(2595, 15632, F25, 33) (dual of [15632, 15537, 34]-code), using
(62, 62+33, large)-Net in Base 25 — Upper bound on s
There is no (62, 95, large)-net in base 25, because
- 31 times m-reduction [i] would yield (62, 64, large)-net in base 25, but