Best Known (182−30, 182, s)-Nets in Base 3
(182−30, 182, 1313)-Net over F3 — Constructive and digital
Digital (152, 182, 1313)-net over F3, using
- net defined by OOA [i] based on linear OOA(3182, 1313, F3, 30, 30) (dual of [(1313, 30), 39208, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3182, 19695, F3, 30) (dual of [19695, 19513, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3182, 19702, F3, 30) (dual of [19702, 19520, 31]-code), using
- construction X applied to Ce(30) ⊂ Ce(27) [i] based on
- linear OA(3181, 19683, F3, 31) (dual of [19683, 19502, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3163, 19683, F3, 28) (dual of [19683, 19520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(31, 19, F3, 1) (dual of [19, 18, 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(30) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(3182, 19702, F3, 30) (dual of [19702, 19520, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(3182, 19695, F3, 30) (dual of [19695, 19513, 31]-code), using
(182−30, 182, 8257)-Net over F3 — Digital
Digital (152, 182, 8257)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3182, 8257, F3, 2, 30) (dual of [(8257, 2), 16332, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3182, 9851, F3, 2, 30) (dual of [(9851, 2), 19520, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3182, 19702, F3, 30) (dual of [19702, 19520, 31]-code), using
- construction X applied to Ce(30) ⊂ Ce(27) [i] based on
- linear OA(3181, 19683, F3, 31) (dual of [19683, 19502, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3163, 19683, F3, 28) (dual of [19683, 19520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(31, 19, F3, 1) (dual of [19, 18, 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(30) ⊂ Ce(27) [i] based on
- OOA 2-folding [i] based on linear OA(3182, 19702, F3, 30) (dual of [19702, 19520, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(3182, 9851, F3, 2, 30) (dual of [(9851, 2), 19520, 31]-NRT-code), using
(182−30, 182, 1976080)-Net in Base 3 — Upper bound on s
There is no (152, 182, 1976081)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 685 597556 978909 260008 779436 201838 958253 006681 252223 048223 879453 399241 336132 280758 182571 > 3182 [i]