Best Known (46, 46+16, s)-Nets in Base 25
(46, 46+16, 48829)-Net over F25 — Constructive and digital
Digital (46, 62, 48829)-net over F25, using
- net defined by OOA [i] based on linear OOA(2562, 48829, F25, 16, 16) (dual of [(48829, 16), 781202, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2562, 390632, F25, 16) (dual of [390632, 390570, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2562, 390634, F25, 16) (dual of [390634, 390572, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(2561, 390625, F25, 16) (dual of [390625, 390564, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2553, 390625, F25, 14) (dual of [390625, 390572, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(2562, 390634, F25, 16) (dual of [390634, 390572, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2562, 390632, F25, 16) (dual of [390632, 390570, 17]-code), using
(46, 46+16, 310643)-Net over F25 — Digital
Digital (46, 62, 310643)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2562, 310643, F25, 16) (dual of [310643, 310581, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2562, 390634, F25, 16) (dual of [390634, 390572, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(2561, 390625, F25, 16) (dual of [390625, 390564, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2553, 390625, F25, 14) (dual of [390625, 390572, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(2562, 390634, F25, 16) (dual of [390634, 390572, 17]-code), using
(46, 46+16, large)-Net in Base 25 — Upper bound on s
There is no (46, 62, large)-net in base 25, because
- 14 times m-reduction [i] would yield (46, 48, large)-net in base 25, but