Best Known (221−25, 221, s)-Nets in Base 3
(221−25, 221, 132865)-Net over F3 — Constructive and digital
Digital (196, 221, 132865)-net over F3, using
- 31 times duplication [i] based on digital (195, 220, 132865)-net over F3, using
- net defined by OOA [i] based on linear OOA(3220, 132865, F3, 25, 25) (dual of [(132865, 25), 3321405, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3220, 1594381, F3, 25) (dual of [1594381, 1594161, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3220, 1594387, F3, 25) (dual of [1594387, 1594167, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3209, 1594324, F3, 25) (dual of [1594324, 1594115, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3157, 1594324, F3, 19) (dual of [1594324, 1594167, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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([0,12]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3220, 1594387, F3, 25) (dual of [1594387, 1594167, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3220, 1594381, F3, 25) (dual of [1594381, 1594161, 26]-code), using
- net defined by OOA [i] based on linear OOA(3220, 132865, F3, 25, 25) (dual of [(132865, 25), 3321405, 26]-NRT-code), using
(221−25, 221, 398597)-Net over F3 — Digital
Digital (196, 221, 398597)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3221, 398597, F3, 4, 25) (dual of [(398597, 4), 1594167, 26]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3221, 1594388, F3, 25) (dual of [1594388, 1594167, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3220, 1594387, F3, 25) (dual of [1594387, 1594167, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3209, 1594324, F3, 25) (dual of [1594324, 1594115, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3157, 1594324, F3, 19) (dual of [1594324, 1594167, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1594324 | 326−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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([0,12]) ⊂ C([0,9]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3220, 1594387, F3, 25) (dual of [1594387, 1594167, 26]-code), using
- OOA 4-folding [i] based on linear OA(3221, 1594388, F3, 25) (dual of [1594388, 1594167, 26]-code), using
(221−25, 221, large)-Net in Base 3 — Upper bound on s
There is no (196, 221, large)-net in base 3, because
- 23 times m-reduction [i] would yield (196, 198, large)-net in base 3, but