Best Known (220, 247, s)-Nets in Base 3
(220, 247, 122645)-Net over F3 — Constructive and digital
Digital (220, 247, 122645)-net over F3, using
- 31 times duplication [i] based on digital (219, 246, 122645)-net over F3, using
- net defined by OOA [i] based on linear OOA(3246, 122645, F3, 27, 27) (dual of [(122645, 27), 3311169, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3246, 1594386, F3, 27) (dual of [1594386, 1594140, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, 1594387, F3, 27) (dual of [1594387, 1594141, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,10]) [i] based on
- linear OA(3235, 1594324, F3, 27) (dual of [1594324, 1594089, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(3183, 1594324, F3, 21) (dual of [1594324, 1594141, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [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 C([0,13]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3246, 1594387, F3, 27) (dual of [1594387, 1594141, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(3246, 1594386, F3, 27) (dual of [1594386, 1594140, 28]-code), using
- net defined by OOA [i] based on linear OOA(3246, 122645, F3, 27, 27) (dual of [(122645, 27), 3311169, 28]-NRT-code), using
(220, 247, 531462)-Net over F3 — Digital
Digital (220, 247, 531462)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3247, 531462, F3, 3, 27) (dual of [(531462, 3), 1594139, 28]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3246, 531462, F3, 3, 27) (dual of [(531462, 3), 1594140, 28]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3246, 1594386, F3, 27) (dual of [1594386, 1594140, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(3246, 1594387, F3, 27) (dual of [1594387, 1594141, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,10]) [i] based on
- linear OA(3235, 1594324, F3, 27) (dual of [1594324, 1594089, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(3183, 1594324, F3, 21) (dual of [1594324, 1594141, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [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 C([0,13]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3246, 1594387, F3, 27) (dual of [1594387, 1594141, 28]-code), using
- OOA 3-folding [i] based on linear OA(3246, 1594386, F3, 27) (dual of [1594386, 1594140, 28]-code), using
- 31 times duplication [i] based on linear OOA(3246, 531462, F3, 3, 27) (dual of [(531462, 3), 1594140, 28]-NRT-code), using
(220, 247, large)-Net in Base 3 — Upper bound on s
There is no (220, 247, large)-net in base 3, because
- 25 times m-reduction [i] would yield (220, 222, large)-net in base 3, but