Best Known (152, 177, s)-Nets in Base 3
(152, 177, 14762)-Net over F3 — Constructive and digital
Digital (152, 177, 14762)-net over F3, using
- net defined by OOA [i] based on linear OOA(3177, 14762, F3, 25, 25) (dual of [(14762, 25), 368873, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3177, 177145, F3, 25) (dual of [177145, 176968, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3177, 177147, F3, 25) (dual of [177147, 176970, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(3177, 177147, F3, 25) (dual of [177147, 176970, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3177, 177145, F3, 25) (dual of [177145, 176968, 26]-code), using
(152, 177, 44287)-Net over F3 — Digital
Digital (152, 177, 44287)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3177, 44287, F3, 4, 25) (dual of [(44287, 4), 176971, 26]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3177, 177148, F3, 25) (dual of [177148, 176971, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- OOA 4-folding [i] based on linear OA(3177, 177148, F3, 25) (dual of [177148, 176971, 26]-code), using
(152, 177, large)-Net in Base 3 — Upper bound on s
There is no (152, 177, large)-net in base 3, because
- 23 times m-reduction [i] would yield (152, 154, large)-net in base 3, but