Best Known (83, 83+12, s)-Nets in Base 3
(83, 83+12, 29531)-Net over F3 — Constructive and digital
Digital (83, 95, 29531)-net over F3, using
- net defined by OOA [i] based on linear OOA(395, 29531, F3, 12, 12) (dual of [(29531, 12), 354277, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(395, 177186, F3, 12) (dual of [177186, 177091, 13]-code), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- 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(356, 177147, F3, 8) (dual of [177147, 177091, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(36, 39, F3, 3) (dual of [39, 33, 4]-code or 39-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 Ce(12) ⊂ Ce(7) [i] based on
- OA 6-folding and stacking [i] based on linear OA(395, 177186, F3, 12) (dual of [177186, 177091, 13]-code), using
(83, 83+12, 88593)-Net over F3 — Digital
Digital (83, 95, 88593)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(395, 88593, F3, 2, 12) (dual of [(88593, 2), 177091, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(395, 177186, F3, 12) (dual of [177186, 177091, 13]-code), using
- construction X applied to Ce(12) ⊂ Ce(7) [i] based on
- 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(356, 177147, F3, 8) (dual of [177147, 177091, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(36, 39, F3, 3) (dual of [39, 33, 4]-code or 39-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 Ce(12) ⊂ Ce(7) [i] based on
- OOA 2-folding [i] based on linear OA(395, 177186, F3, 12) (dual of [177186, 177091, 13]-code), using
(83, 83+12, large)-Net in Base 3 — Upper bound on s
There is no (83, 95, large)-net in base 3, because
- 10 times m-reduction [i] would yield (83, 85, large)-net in base 3, but