Best Known (184, 184+23, s)-Nets in Base 3
(184, 184+23, 144944)-Net over F3 — Constructive and digital
Digital (184, 207, 144944)-net over F3, using
- net defined by OOA [i] based on linear OOA(3207, 144944, F3, 23, 23) (dual of [(144944, 23), 3333505, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3207, 1594385, F3, 23) (dual of [1594385, 1594178, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3207, 1594386, F3, 23) (dual of [1594386, 1594179, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [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(3144, 1594323, F3, 17) (dual of [1594323, 1594179, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(311, 63, F3, 5) (dual of [63, 52, 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(3207, 1594386, F3, 23) (dual of [1594386, 1594179, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(3207, 1594385, F3, 23) (dual of [1594385, 1594178, 24]-code), using
(184, 184+23, 525952)-Net over F3 — Digital
Digital (184, 207, 525952)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3207, 525952, F3, 3, 23) (dual of [(525952, 3), 1577649, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3207, 531462, F3, 3, 23) (dual of [(531462, 3), 1594179, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3207, 1594386, F3, 23) (dual of [1594386, 1594179, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [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(3144, 1594323, F3, 17) (dual of [1594323, 1594179, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(311, 63, F3, 5) (dual of [63, 52, 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
- OOA 3-folding [i] based on linear OA(3207, 1594386, F3, 23) (dual of [1594386, 1594179, 24]-code), using
- discarding factors / shortening the dual code based on linear OOA(3207, 531462, F3, 3, 23) (dual of [(531462, 3), 1594179, 24]-NRT-code), using
(184, 184+23, large)-Net in Base 3 — Upper bound on s
There is no (184, 207, large)-net in base 3, because
- 21 times m-reduction [i] would yield (184, 186, large)-net in base 3, but