Best Known (101, 115, s)-Nets in Base 3
(101, 115, 75926)-Net over F3 — Constructive and digital
Digital (101, 115, 75926)-net over F3, using
- net defined by OOA [i] based on linear OOA(3115, 75926, F3, 14, 14) (dual of [(75926, 14), 1062849, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3115, 531482, F3, 14) (dual of [531482, 531367, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3115, 531483, F3, 14) (dual of [531483, 531368, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(373, 531441, F3, 10) (dual of [531441, 531368, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(36, 42, F3, 3) (dual of [42, 36, 4]-code or 42-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(3115, 531483, F3, 14) (dual of [531483, 531368, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3115, 531482, F3, 14) (dual of [531482, 531367, 15]-code), using
(101, 115, 195568)-Net over F3 — Digital
Digital (101, 115, 195568)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3115, 195568, F3, 2, 14) (dual of [(195568, 2), 391021, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3115, 265741, F3, 2, 14) (dual of [(265741, 2), 531367, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3115, 531482, F3, 14) (dual of [531482, 531367, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3115, 531483, F3, 14) (dual of [531483, 531368, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(373, 531441, F3, 10) (dual of [531441, 531368, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(36, 42, F3, 3) (dual of [42, 36, 4]-code or 42-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(3115, 531483, F3, 14) (dual of [531483, 531368, 15]-code), using
- OOA 2-folding [i] based on linear OA(3115, 531482, F3, 14) (dual of [531482, 531367, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(3115, 265741, F3, 2, 14) (dual of [(265741, 2), 531367, 15]-NRT-code), using
(101, 115, large)-Net in Base 3 — Upper bound on s
There is no (101, 115, large)-net in base 3, because
- 12 times m-reduction [i] would yield (101, 103, large)-net in base 3, but