Best Known (242−28, 242, s)-Nets in Base 3
(242−28, 242, 113882)-Net over F3 — Constructive and digital
Digital (214, 242, 113882)-net over F3, using
- 33 times duplication [i] based on digital (211, 239, 113882)-net over F3, using
- net defined by OOA [i] based on linear OOA(3239, 113882, F3, 28, 28) (dual of [(113882, 28), 3188457, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3239, 1594348, F3, 28) (dual of [1594348, 1594109, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3239, 1594353, F3, 28) (dual of [1594353, 1594114, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(3235, 1594323, F3, 28) (dual of [1594323, 1594088, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3209, 1594323, F3, 25) (dual of [1594323, 1594114, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(34, 30, F3, 2) (dual of [30, 26, 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(27) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(3239, 1594353, F3, 28) (dual of [1594353, 1594114, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3239, 1594348, F3, 28) (dual of [1594348, 1594109, 29]-code), using
- net defined by OOA [i] based on linear OOA(3239, 113882, F3, 28, 28) (dual of [(113882, 28), 3188457, 29]-NRT-code), using
(242−28, 242, 398589)-Net over F3 — Digital
Digital (214, 242, 398589)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3242, 398589, F3, 4, 28) (dual of [(398589, 4), 1594114, 29]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3242, 1594356, F3, 28) (dual of [1594356, 1594114, 29]-code), using
- 3 times code embedding in larger space [i] based on linear OA(3239, 1594353, F3, 28) (dual of [1594353, 1594114, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(3235, 1594323, F3, 28) (dual of [1594323, 1594088, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3209, 1594323, F3, 25) (dual of [1594323, 1594114, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(34, 30, F3, 2) (dual of [30, 26, 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(27) ⊂ Ce(24) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(3239, 1594353, F3, 28) (dual of [1594353, 1594114, 29]-code), using
- OOA 4-folding [i] based on linear OA(3242, 1594356, F3, 28) (dual of [1594356, 1594114, 29]-code), using
(242−28, 242, large)-Net in Base 3 — Upper bound on s
There is no (214, 242, large)-net in base 3, because
- 26 times m-reduction [i] would yield (214, 216, large)-net in base 3, but