Best Known (46−12, 46, s)-Nets in Base 25
(46−12, 46, 65105)-Net over F25 — Constructive and digital
Digital (34, 46, 65105)-net over F25, using
- net defined by OOA [i] based on linear OOA(2546, 65105, F25, 12, 12) (dual of [(65105, 12), 781214, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2546, 390630, F25, 12) (dual of [390630, 390584, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2546, 390634, F25, 12) (dual of [390634, 390588, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(2545, 390625, F25, 12) (dual of [390625, 390580, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2537, 390625, F25, 10) (dual of [390625, 390588, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(251, 9, F25, 1) (dual of [9, 8, 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(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(2546, 390634, F25, 12) (dual of [390634, 390588, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2546, 390630, F25, 12) (dual of [390630, 390584, 13]-code), using
(46−12, 46, 368544)-Net over F25 — Digital
Digital (34, 46, 368544)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2546, 368544, F25, 12) (dual of [368544, 368498, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2546, 390634, F25, 12) (dual of [390634, 390588, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(2545, 390625, F25, 12) (dual of [390625, 390580, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2537, 390625, F25, 10) (dual of [390625, 390588, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(251, 9, F25, 1) (dual of [9, 8, 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(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(2546, 390634, F25, 12) (dual of [390634, 390588, 13]-code), using
(46−12, 46, large)-Net in Base 25 — Upper bound on s
There is no (34, 46, large)-net in base 25, because
- 10 times m-reduction [i] would yield (34, 36, large)-net in base 25, but