Best Known (192−23, 192, s)-Nets in Base 3
(192−23, 192, 48318)-Net over F3 — Constructive and digital
Digital (169, 192, 48318)-net over F3, using
- net defined by OOA [i] based on linear OOA(3192, 48318, F3, 23, 23) (dual of [(48318, 23), 1111122, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3192, 531499, F3, 23) (dual of [531499, 531307, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3192, 531500, F3, 23) (dual of [531500, 531308, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(3181, 531441, F3, 23) (dual of [531441, 531260, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(311, 59, F3, 5) (dual of [59, 48, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3192, 531500, F3, 23) (dual of [531500, 531308, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3192, 531499, F3, 23) (dual of [531499, 531307, 24]-code), using
(192−23, 192, 177166)-Net over F3 — Digital
Digital (169, 192, 177166)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3192, 177166, F3, 3, 23) (dual of [(177166, 3), 531306, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3192, 531498, F3, 23) (dual of [531498, 531306, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3192, 531500, F3, 23) (dual of [531500, 531308, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(3181, 531441, F3, 23) (dual of [531441, 531260, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(311, 59, F3, 5) (dual of [59, 48, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3192, 531500, F3, 23) (dual of [531500, 531308, 24]-code), using
- OOA 3-folding [i] based on linear OA(3192, 531498, F3, 23) (dual of [531498, 531306, 24]-code), using
(192−23, 192, large)-Net in Base 3 — Upper bound on s
There is no (169, 192, large)-net in base 3, because
- 21 times m-reduction [i] would yield (169, 171, large)-net in base 3, but