Best Known (193, 193+28, s)-Nets in Base 3
(193, 193+28, 37962)-Net over F3 — Constructive and digital
Digital (193, 221, 37962)-net over F3, using
- net defined by OOA [i] based on linear OOA(3221, 37962, F3, 28, 28) (dual of [(37962, 28), 1062715, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3221, 531468, F3, 28) (dual of [531468, 531247, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3221, 531469, F3, 28) (dual of [531469, 531248, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(3217, 531441, F3, 28) (dual of [531441, 531224, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3193, 531441, F3, 25) (dual of [531441, 531248, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(27) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(3221, 531469, F3, 28) (dual of [531469, 531248, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3221, 531468, F3, 28) (dual of [531468, 531247, 29]-code), using
(193, 193+28, 132867)-Net over F3 — Digital
Digital (193, 221, 132867)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3221, 132867, F3, 4, 28) (dual of [(132867, 4), 531247, 29]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3221, 531468, F3, 28) (dual of [531468, 531247, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3221, 531469, F3, 28) (dual of [531469, 531248, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(3217, 531441, F3, 28) (dual of [531441, 531224, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3193, 531441, F3, 25) (dual of [531441, 531248, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(27) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(3221, 531469, F3, 28) (dual of [531469, 531248, 29]-code), using
- OOA 4-folding [i] based on linear OA(3221, 531468, F3, 28) (dual of [531468, 531247, 29]-code), using
(193, 193+28, large)-Net in Base 3 — Upper bound on s
There is no (193, 221, large)-net in base 3, because
- 26 times m-reduction [i] would yield (193, 195, large)-net in base 3, but