Best Known (124, 124+8, s)-Nets in Base 3
(124, 124+8, large)-Net over F3 — Constructive and digital
Digital (124, 132, large)-net over F3, using
- trace code for nets [i] based on digital (25, 33, 2097231)-net over F81, using
- net defined by OOA [i] based on linear OOA(8133, 2097231, F81, 12, 8) (dual of [(2097231, 12), 25166739, 9]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(8133, 2097232, F81, 4, 8) (dual of [(2097232, 4), 8388895, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(814, 82, F81, 4, 4) (dual of [(82, 4), 324, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;324,81) [i]
- linear OOA(8129, 2097150, F81, 4, 8) (dual of [(2097150, 4), 8388571, 9]-NRT-code), using
- OOA 4-folding [i] based on linear OA(8129, 8388600, F81, 8) (dual of [8388600, 8388571, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(8129, large, F81, 8) (dual of [large, large−29, 9]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(8129, large, F81, 8) (dual of [large, large−29, 9]-code), using
- OOA 4-folding [i] based on linear OA(8129, 8388600, F81, 8) (dual of [8388600, 8388571, 9]-code), using
- linear OOA(814, 82, F81, 4, 4) (dual of [(82, 4), 324, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(8133, 2097232, F81, 4, 8) (dual of [(2097232, 4), 8388895, 9]-NRT-code), using
- net defined by OOA [i] based on linear OOA(8133, 2097231, F81, 12, 8) (dual of [(2097231, 12), 25166739, 9]-NRT-code), using
(124, 124+8, large)-Net in Base 3 — Upper bound on s
There is no (124, 132, large)-net in base 3, because
- 6 times m-reduction [i] would yield (124, 126, large)-net in base 3, but