Best Known (88, 101, s)-Nets in Base 3
(88, 101, 88578)-Net over F3 — Constructive and digital
Digital (88, 101, 88578)-net over F3, using
- net defined by OOA [i] based on linear OOA(3101, 88578, F3, 13, 13) (dual of [(88578, 13), 1151413, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3101, 531469, F3, 13) (dual of [531469, 531368, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(397, 531441, F3, 13) (dual of [531441, 531344, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(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(12) ⊂ Ce(9) [i] based on
- OOA 6-folding and stacking with additional row [i] based on linear OA(3101, 531469, F3, 13) (dual of [531469, 531368, 14]-code), using
(88, 101, 177156)-Net over F3 — Digital
Digital (88, 101, 177156)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3101, 177156, F3, 3, 13) (dual of [(177156, 3), 531367, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3101, 531468, F3, 13) (dual of [531468, 531367, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(3101, 531469, F3, 13) (dual of [531469, 531368, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(397, 531441, F3, 13) (dual of [531441, 531344, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(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(12) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(3101, 531469, F3, 13) (dual of [531469, 531368, 14]-code), using
- OOA 3-folding [i] based on linear OA(3101, 531468, F3, 13) (dual of [531468, 531367, 14]-code), using
(88, 101, large)-Net in Base 3 — Upper bound on s
There is no (88, 101, large)-net in base 3, because
- 11 times m-reduction [i] would yield (88, 90, large)-net in base 3, but