Best Known (14, 28, s)-Nets in Base 81
(14, 28, 938)-Net over F81 — Constructive and digital
Digital (14, 28, 938)-net over F81, using
- net defined by OOA [i] based on linear OOA(8128, 938, F81, 14, 14) (dual of [(938, 14), 13104, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(8128, 6566, F81, 14) (dual of [6566, 6538, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(8123, 6561, F81, 12) (dual of [6561, 6538, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- OA 7-folding and stacking [i] based on linear OA(8128, 6566, F81, 14) (dual of [6566, 6538, 15]-code), using
(14, 28, 2188)-Net over F81 — Digital
Digital (14, 28, 2188)-net over F81, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8128, 2188, F81, 3, 14) (dual of [(2188, 3), 6536, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8128, 6564, F81, 14) (dual of [6564, 6536, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(8128, 6566, F81, 14) (dual of [6566, 6538, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(8123, 6561, F81, 12) (dual of [6561, 6538, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(8128, 6566, F81, 14) (dual of [6566, 6538, 15]-code), using
- OOA 3-folding [i] based on linear OA(8128, 6564, F81, 14) (dual of [6564, 6536, 15]-code), using
(14, 28, 1818729)-Net in Base 81 — Upper bound on s
There is no (14, 28, 1818730)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 273893 765808 130088 921225 713444 232332 126042 310856 024801 > 8128 [i]