Best Known (85−14, 85, s)-Nets in Base 3
(85−14, 85, 2813)-Net over F3 — Constructive and digital
Digital (71, 85, 2813)-net over F3, using
- 33 times duplication [i] based on digital (68, 82, 2813)-net over F3, using
- net defined by OOA [i] based on linear OOA(382, 2813, F3, 14, 14) (dual of [(2813, 14), 39300, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(382, 19691, F3, 14) (dual of [19691, 19609, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(382, 19692, F3, 14) (dual of [19692, 19610, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(382, 19683, F3, 14) (dual of [19683, 19601, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(373, 19683, F3, 13) (dual of [19683, 19610, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(30, 9, F3, 0) (dual of [9, 9, 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(382, 19692, F3, 14) (dual of [19692, 19610, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(382, 19691, F3, 14) (dual of [19691, 19609, 15]-code), using
- net defined by OOA [i] based on linear OOA(382, 2813, F3, 14, 14) (dual of [(2813, 14), 39300, 15]-NRT-code), using
(85−14, 85, 9764)-Net over F3 — Digital
Digital (71, 85, 9764)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(385, 9764, F3, 2, 14) (dual of [(9764, 2), 19443, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(385, 9848, F3, 2, 14) (dual of [(9848, 2), 19611, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(385, 19696, F3, 14) (dual of [19696, 19611, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(382, 19683, F3, 14) (dual of [19683, 19601, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(364, 19683, F3, 11) (dual of [19683, 19619, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(33, 13, F3, 2) (dual of [13, 10, 3]-code), using
- Hamming code H(3,3) [i]
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- OOA 2-folding [i] based on linear OA(385, 19696, F3, 14) (dual of [19696, 19611, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(385, 9848, F3, 2, 14) (dual of [(9848, 2), 19611, 15]-NRT-code), using
(85−14, 85, 1050754)-Net in Base 3 — Upper bound on s
There is no (71, 85, 1050755)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 35917 698109 526663 502653 462646 347682 501123 > 385 [i]