Best Known (96, 112, s)-Nets in Base 3
(96, 112, 22144)-Net over F3 — Constructive and digital
Digital (96, 112, 22144)-net over F3, using
- net defined by OOA [i] based on linear OOA(3112, 22144, F3, 16, 16) (dual of [(22144, 16), 354192, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(3112, 177152, F3, 16) (dual of [177152, 177040, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(3112, 177159, F3, 16) (dual of [177159, 177047, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3100, 177147, F3, 14) (dual of [177147, 177047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 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(3112, 177159, F3, 16) (dual of [177159, 177047, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(3112, 177152, F3, 16) (dual of [177152, 177040, 17]-code), using
(96, 112, 57029)-Net over F3 — Digital
Digital (96, 112, 57029)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3112, 57029, F3, 3, 16) (dual of [(57029, 3), 170975, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3112, 59053, F3, 3, 16) (dual of [(59053, 3), 177047, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3112, 177159, F3, 16) (dual of [177159, 177047, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(3111, 177147, F3, 16) (dual of [177147, 177036, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(3100, 177147, F3, 14) (dual of [177147, 177047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- OOA 3-folding [i] based on linear OA(3112, 177159, F3, 16) (dual of [177159, 177047, 17]-code), using
- discarding factors / shortening the dual code based on linear OOA(3112, 59053, F3, 3, 16) (dual of [(59053, 3), 177047, 17]-NRT-code), using
(96, 112, large)-Net in Base 3 — Upper bound on s
There is no (96, 112, large)-net in base 3, because
- 14 times m-reduction [i] would yield (96, 98, large)-net in base 3, but