Best Known (187, 221, s)-Nets in Base 3
(187, 221, 3473)-Net over F3 — Constructive and digital
Digital (187, 221, 3473)-net over F3, using
- net defined by OOA [i] based on linear OOA(3221, 3473, F3, 34, 34) (dual of [(3473, 34), 117861, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(3221, 59041, F3, 34) (dual of [59041, 58820, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- discarding factors / shortening the dual code based on linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(3221, 59041, F3, 34) (dual of [59041, 58820, 35]-code), using
(187, 221, 17625)-Net over F3 — Digital
Digital (187, 221, 17625)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3221, 17625, F3, 3, 34) (dual of [(17625, 3), 52654, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3221, 19683, F3, 3, 34) (dual of [(19683, 3), 58828, 35]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using
- an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- OOA 3-folding [i] based on linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using
- discarding factors / shortening the dual code based on linear OOA(3221, 19683, F3, 3, 34) (dual of [(19683, 3), 58828, 35]-NRT-code), using
(187, 221, 5721241)-Net in Base 3 — Upper bound on s
There is no (187, 221, 5721242)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2778 421380 842358 140963 267787 872744 285250 677786 723740 438841 392052 496674 478913 463509 986484 573737 523529 771925 > 3221 [i]