Best Known (121, 138, s)-Nets in Base 3
(121, 138, 66433)-Net over F3 — Constructive and digital
Digital (121, 138, 66433)-net over F3, using
- 31 times duplication [i] based on digital (120, 137, 66433)-net over F3, using
- net defined by OOA [i] based on linear OOA(3137, 66433, F3, 17, 17) (dual of [(66433, 17), 1129224, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3137, 531465, F3, 17) (dual of [531465, 531328, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3137, 531469, F3, 17) (dual of [531469, 531332, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(3133, 531441, F3, 17) (dual of [531441, 531308, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 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(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(16) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3137, 531469, F3, 17) (dual of [531469, 531332, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3137, 531465, F3, 17) (dual of [531465, 531328, 18]-code), using
- net defined by OOA [i] based on linear OOA(3137, 66433, F3, 17, 17) (dual of [(66433, 17), 1129224, 18]-NRT-code), using
(121, 138, 177156)-Net over F3 — Digital
Digital (121, 138, 177156)-net over F3, using
- 31 times duplication [i] based on digital (120, 137, 177156)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3137, 177156, F3, 3, 17) (dual of [(177156, 3), 531331, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3137, 531468, F3, 17) (dual of [531468, 531331, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3137, 531469, F3, 17) (dual of [531469, 531332, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(3133, 531441, F3, 17) (dual of [531441, 531308, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 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(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(16) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(3137, 531469, F3, 17) (dual of [531469, 531332, 18]-code), using
- OOA 3-folding [i] based on linear OA(3137, 531468, F3, 17) (dual of [531468, 531331, 18]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3137, 177156, F3, 3, 17) (dual of [(177156, 3), 531331, 18]-NRT-code), using
(121, 138, large)-Net in Base 3 — Upper bound on s
There is no (121, 138, large)-net in base 3, because
- 15 times m-reduction [i] would yield (121, 123, large)-net in base 3, but