Best Known (139, 148, s)-Nets in Base 3
(139, 148, large)-Net over F3 — Constructive and digital
Digital (139, 148, large)-net over F3, using
- trace code for nets [i] based on digital (28, 37, 2097231)-net over F81, using
- net defined by OOA [i] based on linear OOA(8137, 2097231, F81, 12, 9) (dual of [(2097231, 12), 25166735, 10]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(8137, 2097232, F81, 4, 9) (dual of [(2097232, 4), 8388891, 10]-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(8133, 2097150, F81, 4, 9) (dual of [(2097150, 4), 8388567, 10]-NRT-code), using
- OOA 4-folding [i] based on linear OA(8133, 8388600, F81, 9) (dual of [8388600, 8388567, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
- OOA 4-folding [i] based on linear OA(8133, 8388600, F81, 9) (dual of [8388600, 8388567, 10]-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(8137, 2097232, F81, 4, 9) (dual of [(2097232, 4), 8388891, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(8137, 2097231, F81, 12, 9) (dual of [(2097231, 12), 25166735, 10]-NRT-code), using
(139, 148, large)-Net in Base 3 — Upper bound on s
There is no (139, 148, large)-net in base 3, because
- 7 times m-reduction [i] would yield (139, 141, large)-net in base 3, but