Best Known (126, 145, s)-Nets in Base 3
(126, 145, 59049)-Net over F3 — Constructive and digital
Digital (126, 145, 59049)-net over F3, using
- net defined by OOA [i] based on linear OOA(3145, 59049, F3, 19, 19) (dual of [(59049, 19), 1121786, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3145, 531442, F3, 19) (dual of [531442, 531297, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(3145, 531442, F3, 19) (dual of [531442, 531297, 20]-code), using
(126, 145, 132860)-Net over F3 — Digital
Digital (126, 145, 132860)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3145, 132860, F3, 4, 19) (dual of [(132860, 4), 531295, 20]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3145, 531440, F3, 19) (dual of [531440, 531295, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3145, 531441, F3, 19) (dual of [531441, 531296, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(3145, 531441, F3, 19) (dual of [531441, 531296, 20]-code), using
- OOA 4-folding [i] based on linear OA(3145, 531440, F3, 19) (dual of [531440, 531295, 20]-code), using
(126, 145, large)-Net in Base 3 — Upper bound on s
There is no (126, 145, large)-net in base 3, because
- 17 times m-reduction [i] would yield (126, 128, large)-net in base 3, but