Best Known (200−23, 200, s)-Nets in Base 3
(200−23, 200, 144941)-Net over F3 — Constructive and digital
Digital (177, 200, 144941)-net over F3, using
- net defined by OOA [i] based on linear OOA(3200, 144941, F3, 23, 23) (dual of [(144941, 23), 3333443, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3200, 1594352, F3, 23) (dual of [1594352, 1594152, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3200, 1594353, F3, 23) (dual of [1594353, 1594153, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(3196, 1594323, F3, 23) (dual of [1594323, 1594127, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3170, 1594323, F3, 20) (dual of [1594323, 1594153, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(22) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3200, 1594353, F3, 23) (dual of [1594353, 1594153, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3200, 1594352, F3, 23) (dual of [1594352, 1594152, 24]-code), using
(200−23, 200, 398588)-Net over F3 — Digital
Digital (177, 200, 398588)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3200, 398588, F3, 4, 23) (dual of [(398588, 4), 1594152, 24]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3200, 1594352, F3, 23) (dual of [1594352, 1594152, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3200, 1594353, F3, 23) (dual of [1594353, 1594153, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(3196, 1594323, F3, 23) (dual of [1594323, 1594127, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(3170, 1594323, F3, 20) (dual of [1594323, 1594153, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(22) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3200, 1594353, F3, 23) (dual of [1594353, 1594153, 24]-code), using
- OOA 4-folding [i] based on linear OA(3200, 1594352, F3, 23) (dual of [1594352, 1594152, 24]-code), using
(200−23, 200, large)-Net in Base 3 — Upper bound on s
There is no (177, 200, large)-net in base 3, because
- 21 times m-reduction [i] would yield (177, 179, large)-net in base 3, but