Best Known (169, 194, s)-Nets in Base 3
(169, 194, 44287)-Net over F3 — Constructive and digital
Digital (169, 194, 44287)-net over F3, using
- net defined by OOA [i] based on linear OOA(3194, 44287, F3, 25, 25) (dual of [(44287, 25), 1106981, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3194, 531445, F3, 25) (dual of [531445, 531251, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3194, 531454, F3, 25) (dual of [531454, 531260, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- 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(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(31, 13, F3, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(3194, 531454, F3, 25) (dual of [531454, 531260, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3194, 531445, F3, 25) (dual of [531445, 531251, 26]-code), using
(169, 194, 132863)-Net over F3 — Digital
Digital (169, 194, 132863)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3194, 132863, F3, 4, 25) (dual of [(132863, 4), 531258, 26]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3194, 531452, F3, 25) (dual of [531452, 531258, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3194, 531454, F3, 25) (dual of [531454, 531260, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- 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(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(31, 13, F3, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(3194, 531454, F3, 25) (dual of [531454, 531260, 26]-code), using
- OOA 4-folding [i] based on linear OA(3194, 531452, F3, 25) (dual of [531452, 531258, 26]-code), using
(169, 194, large)-Net in Base 3 — Upper bound on s
There is no (169, 194, large)-net in base 3, because
- 23 times m-reduction [i] would yield (169, 171, large)-net in base 3, but