Best Known (190, 216, s)-Nets in Base 3
(190, 216, 40884)-Net over F3 — Constructive and digital
Digital (190, 216, 40884)-net over F3, using
- net defined by OOA [i] based on linear OOA(3216, 40884, F3, 26, 26) (dual of [(40884, 26), 1062768, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3216, 531492, F3, 26) (dual of [531492, 531276, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3216, 531500, F3, 26) (dual of [531500, 531284, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(3205, 531441, F3, 26) (dual of [531441, 531236, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3157, 531441, F3, 20) (dual of [531441, 531284, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(25) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3216, 531500, F3, 26) (dual of [531500, 531284, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3216, 531492, F3, 26) (dual of [531492, 531276, 27]-code), using
(190, 216, 177166)-Net over F3 — Digital
Digital (190, 216, 177166)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3216, 177166, F3, 3, 26) (dual of [(177166, 3), 531282, 27]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3216, 531498, F3, 26) (dual of [531498, 531282, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3216, 531500, F3, 26) (dual of [531500, 531284, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(3205, 531441, F3, 26) (dual of [531441, 531236, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3157, 531441, F3, 20) (dual of [531441, 531284, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(25) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3216, 531500, F3, 26) (dual of [531500, 531284, 27]-code), using
- OOA 3-folding [i] based on linear OA(3216, 531498, F3, 26) (dual of [531498, 531282, 27]-code), using
(190, 216, large)-Net in Base 3 — Upper bound on s
There is no (190, 216, large)-net in base 3, because
- 24 times m-reduction [i] would yield (190, 192, large)-net in base 3, but