Best Known (243−25, 243, s)-Nets in Base 3
(243−25, 243, 699050)-Net over F3 — Constructive and digital
Digital (218, 243, 699050)-net over F3, using
- 32 times duplication [i] based on digital (216, 241, 699050)-net over F3, using
- net defined by OOA [i] based on linear OOA(3241, 699050, F3, 25, 25) (dual of [(699050, 25), 17476009, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3241, 8388601, F3, 25) (dual of [8388601, 8388360, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, large, F3, 25) (dual of [large, large−241, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3241, large, F3, 25) (dual of [large, large−241, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3241, 8388601, F3, 25) (dual of [8388601, 8388360, 26]-code), using
- net defined by OOA [i] based on linear OOA(3241, 699050, F3, 25, 25) (dual of [(699050, 25), 17476009, 26]-NRT-code), using
(243−25, 243, 2088677)-Net over F3 — Digital
Digital (218, 243, 2088677)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3243, 2088677, F3, 4, 25) (dual of [(2088677, 4), 8354465, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3243, 2097151, F3, 4, 25) (dual of [(2097151, 4), 8388361, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3243, 4194302, F3, 2, 25) (dual of [(4194302, 2), 8388361, 26]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3241, 4194301, F3, 2, 25) (dual of [(4194301, 2), 8388361, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3241, 8388602, F3, 25) (dual of [8388602, 8388361, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3241, large, F3, 25) (dual of [large, large−241, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3241, large, F3, 25) (dual of [large, large−241, 26]-code), using
- OOA 2-folding [i] based on linear OA(3241, 8388602, F3, 25) (dual of [8388602, 8388361, 26]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3241, 4194301, F3, 2, 25) (dual of [(4194301, 2), 8388361, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3243, 4194302, F3, 2, 25) (dual of [(4194302, 2), 8388361, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3243, 2097151, F3, 4, 25) (dual of [(2097151, 4), 8388361, 26]-NRT-code), using
(243−25, 243, large)-Net in Base 3 — Upper bound on s
There is no (218, 243, large)-net in base 3, because
- 23 times m-reduction [i] would yield (218, 220, large)-net in base 3, but