Best Known (150, 150+30, s)-Nets in Base 3
(150, 150+30, 1312)-Net over F3 — Constructive and digital
Digital (150, 180, 1312)-net over F3, using
- net defined by OOA [i] based on linear OOA(3180, 1312, F3, 30, 30) (dual of [(1312, 30), 39180, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3180, 19680, F3, 30) (dual of [19680, 19500, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3180, 19683, F3, 30) (dual of [19683, 19503, 31]-code), using
- 1 times truncation [i] based on linear OA(3181, 19684, F3, 31) (dual of [19684, 19503, 32]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3181, 19684, F3, 31) (dual of [19684, 19503, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3180, 19683, F3, 30) (dual of [19683, 19503, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(3180, 19680, F3, 30) (dual of [19680, 19500, 31]-code), using
(150, 150+30, 7610)-Net over F3 — Digital
Digital (150, 180, 7610)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3180, 7610, F3, 2, 30) (dual of [(7610, 2), 15040, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3180, 9841, F3, 2, 30) (dual of [(9841, 2), 19502, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3180, 19682, F3, 30) (dual of [19682, 19502, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3180, 19683, F3, 30) (dual of [19683, 19503, 31]-code), using
- 1 times truncation [i] based on linear OA(3181, 19684, F3, 31) (dual of [19684, 19503, 32]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3181, 19684, F3, 31) (dual of [19684, 19503, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3180, 19683, F3, 30) (dual of [19683, 19503, 31]-code), using
- OOA 2-folding [i] based on linear OA(3180, 19682, F3, 30) (dual of [19682, 19502, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(3180, 9841, F3, 2, 30) (dual of [(9841, 2), 19502, 31]-NRT-code), using
(150, 150+30, 1706821)-Net in Base 3 — Upper bound on s
There is no (150, 180, 1706822)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 76 177926 277976 006557 807160 974387 816933 251335 918347 158269 628880 528979 093817 900321 305801 > 3180 [i]