Best Known (216, 216+25, s)-Nets in Base 3
(216, 216+25, 699050)-Net over F3 — Constructive and digital
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
(216, 216+25, 1871366)-Net over F3 — Digital
Digital (216, 241, 1871366)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3241, 1871366, F3, 4, 25) (dual of [(1871366, 4), 7485223, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3241, 2097150, F3, 4, 25) (dual of [(2097150, 4), 8388359, 26]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3241, 8388600, F3, 25) (dual of [8388600, 8388359, 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 4-folding [i] based on linear OA(3241, 8388600, F3, 25) (dual of [8388600, 8388359, 26]-code), using
- discarding factors / shortening the dual code based on linear OOA(3241, 2097150, F3, 4, 25) (dual of [(2097150, 4), 8388359, 26]-NRT-code), using
(216, 216+25, large)-Net in Base 3 — Upper bound on s
There is no (216, 241, large)-net in base 3, because
- 23 times m-reduction [i] would yield (216, 218, large)-net in base 3, but