Best Known (110, 124, s)-Nets in Base 3
(110, 124, 227766)-Net over F3 — Constructive and digital
Digital (110, 124, 227766)-net over F3, using
- net defined by OOA [i] based on linear OOA(3124, 227766, F3, 14, 14) (dual of [(227766, 14), 3188600, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3124, 1594362, F3, 14) (dual of [1594362, 1594238, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3124, 1594368, F3, 14) (dual of [1594368, 1594244, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(3118, 1594323, F3, 14) (dual of [1594323, 1594205, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(379, 1594323, F3, 10) (dual of [1594323, 1594244, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(36, 45, F3, 3) (dual of [45, 39, 4]-code or 45-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(3124, 1594368, F3, 14) (dual of [1594368, 1594244, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3124, 1594362, F3, 14) (dual of [1594362, 1594238, 15]-code), using
(110, 124, 531456)-Net over F3 — Digital
Digital (110, 124, 531456)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3124, 531456, F3, 3, 14) (dual of [(531456, 3), 1594244, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3124, 1594368, F3, 14) (dual of [1594368, 1594244, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(3118, 1594323, F3, 14) (dual of [1594323, 1594205, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(379, 1594323, F3, 10) (dual of [1594323, 1594244, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(36, 45, F3, 3) (dual of [45, 39, 4]-code or 45-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 3-folding [i] based on linear OA(3124, 1594368, F3, 14) (dual of [1594368, 1594244, 15]-code), using
(110, 124, large)-Net in Base 3 — Upper bound on s
There is no (110, 124, large)-net in base 3, because
- 12 times m-reduction [i] would yield (110, 112, large)-net in base 3, but