Best Known (82, 82+13, s)-Nets in Base 3
(82, 82+13, 29529)-Net over F3 — Constructive and digital
Digital (82, 95, 29529)-net over F3, using
- net defined by OOA [i] based on linear OOA(395, 29529, F3, 13, 13) (dual of [(29529, 13), 383782, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(395, 177175, F3, 13) (dual of [177175, 177080, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(395, 177176, F3, 13) (dual of [177176, 177081, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- linear OA(389, 177148, F3, 13) (dual of [177148, 177059, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(367, 177148, F3, 9) (dual of [177148, 177081, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(36, 28, F3, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- discarding factors / shortening the dual code based on linear OA(395, 177176, F3, 13) (dual of [177176, 177081, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(395, 177175, F3, 13) (dual of [177175, 177080, 14]-code), using
(82, 82+13, 61960)-Net over F3 — Digital
Digital (82, 95, 61960)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(395, 61960, F3, 2, 13) (dual of [(61960, 2), 123825, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(395, 88588, F3, 2, 13) (dual of [(88588, 2), 177081, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(395, 177176, F3, 13) (dual of [177176, 177081, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- linear OA(389, 177148, F3, 13) (dual of [177148, 177059, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(367, 177148, F3, 9) (dual of [177148, 177081, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(36, 28, F3, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
- OOA 2-folding [i] based on linear OA(395, 177176, F3, 13) (dual of [177176, 177081, 14]-code), using
- discarding factors / shortening the dual code based on linear OOA(395, 88588, F3, 2, 13) (dual of [(88588, 2), 177081, 14]-NRT-code), using
(82, 82+13, large)-Net in Base 3 — Upper bound on s
There is no (82, 95, large)-net in base 3, because
- 11 times m-reduction [i] would yield (82, 84, large)-net in base 3, but