Best Known (107−14, 107, s)-Nets in Base 3
(107−14, 107, 25312)-Net over F3 — Constructive and digital
Digital (93, 107, 25312)-net over F3, using
- 31 times duplication [i] based on digital (92, 106, 25312)-net over F3, using
- net defined by OOA [i] based on linear OOA(3106, 25312, F3, 14, 14) (dual of [(25312, 14), 354262, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3106, 177184, F3, 14) (dual of [177184, 177078, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3106, 177186, F3, 14) (dual of [177186, 177080, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(3100, 177147, F3, 14) (dual of [177147, 177047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(367, 177147, F3, 10) (dual of [177147, 177080, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(13) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(3106, 177186, F3, 14) (dual of [177186, 177080, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3106, 177184, F3, 14) (dual of [177184, 177078, 15]-code), using
- net defined by OOA [i] based on linear OOA(3106, 25312, F3, 14, 14) (dual of [(25312, 14), 354262, 15]-NRT-code), using
(107−14, 107, 87958)-Net over F3 — Digital
Digital (93, 107, 87958)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3107, 87958, F3, 2, 14) (dual of [(87958, 2), 175809, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3107, 88593, F3, 2, 14) (dual of [(88593, 2), 177079, 15]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3106, 88593, F3, 2, 14) (dual of [(88593, 2), 177080, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3106, 177186, F3, 14) (dual of [177186, 177080, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(3100, 177147, F3, 14) (dual of [177147, 177047, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(367, 177147, F3, 10) (dual of [177147, 177080, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(13) ⊂ Ce(9) [i] based on
- OOA 2-folding [i] based on linear OA(3106, 177186, F3, 14) (dual of [177186, 177080, 15]-code), using
- 31 times duplication [i] based on linear OOA(3106, 88593, F3, 2, 14) (dual of [(88593, 2), 177080, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3107, 88593, F3, 2, 14) (dual of [(88593, 2), 177079, 15]-NRT-code), using
(107−14, 107, large)-Net in Base 3 — Upper bound on s
There is no (93, 107, large)-net in base 3, because
- 12 times m-reduction [i] would yield (93, 95, large)-net in base 3, but