Best Known (86, 100, s)-Nets in Base 3
(86, 100, 25308)-Net over F3 — Constructive and digital
Digital (86, 100, 25308)-net over F3, using
- net defined by OOA [i] based on linear OOA(3100, 25308, F3, 14, 14) (dual of [(25308, 14), 354212, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3100, 177156, F3, 14) (dual of [177156, 177056, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3100, 177158, F3, 14) (dual of [177158, 177058, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- 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(389, 177147, F3, 13) (dual of [177147, 177058, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(30, 11, F3, 0) (dual of [11, 11, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3100, 177158, F3, 14) (dual of [177158, 177058, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3100, 177156, F3, 14) (dual of [177156, 177056, 15]-code), using
(86, 100, 59052)-Net over F3 — Digital
Digital (86, 100, 59052)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3100, 59052, F3, 3, 14) (dual of [(59052, 3), 177056, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3100, 177156, F3, 14) (dual of [177156, 177056, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3100, 177158, F3, 14) (dual of [177158, 177058, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- 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(389, 177147, F3, 13) (dual of [177147, 177058, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(30, 11, F3, 0) (dual of [11, 11, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3100, 177158, F3, 14) (dual of [177158, 177058, 15]-code), using
- OOA 3-folding [i] based on linear OA(3100, 177156, F3, 14) (dual of [177156, 177056, 15]-code), using
(86, 100, large)-Net in Base 3 — Upper bound on s
There is no (86, 100, large)-net in base 3, because
- 12 times m-reduction [i] would yield (86, 88, large)-net in base 3, but