Best Known (99, 113, s)-Nets in Base 3
(99, 113, 75924)-Net over F3 — Constructive and digital
Digital (99, 113, 75924)-net over F3, using
- net defined by OOA [i] based on linear OOA(3113, 75924, F3, 14, 14) (dual of [(75924, 14), 1062823, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3113, 531468, F3, 14) (dual of [531468, 531355, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3113, 531469, F3, 14) (dual of [531469, 531356, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [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(385, 531441, F3, 11) (dual of [531441, 531356, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(34, 28, F3, 2) (dual of [28, 24, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(3113, 531469, F3, 14) (dual of [531469, 531356, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3113, 531468, F3, 14) (dual of [531468, 531355, 15]-code), using
(99, 113, 177156)-Net over F3 — Digital
Digital (99, 113, 177156)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3113, 177156, F3, 3, 14) (dual of [(177156, 3), 531355, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3113, 531468, F3, 14) (dual of [531468, 531355, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3113, 531469, F3, 14) (dual of [531469, 531356, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [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(385, 531441, F3, 11) (dual of [531441, 531356, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(34, 28, F3, 2) (dual of [28, 24, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(3113, 531469, F3, 14) (dual of [531469, 531356, 15]-code), using
- OOA 3-folding [i] based on linear OA(3113, 531468, F3, 14) (dual of [531468, 531355, 15]-code), using
(99, 113, large)-Net in Base 3 — Upper bound on s
There is no (99, 113, large)-net in base 3, because
- 12 times m-reduction [i] would yield (99, 101, large)-net in base 3, but