Best Known (144−24, 144, s)-Nets in Base 3
(144−24, 144, 1640)-Net over F3 — Constructive and digital
Digital (120, 144, 1640)-net over F3, using
- net defined by OOA [i] based on linear OOA(3144, 1640, F3, 24, 24) (dual of [(1640, 24), 39216, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3144, 19680, F3, 24) (dual of [19680, 19536, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3144, 19683, F3, 24) (dual of [19683, 19539, 25]-code), using
- 1 times truncation [i] based on linear OA(3145, 19684, F3, 25) (dual of [19684, 19539, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3145, 19684, F3, 25) (dual of [19684, 19539, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3144, 19683, F3, 24) (dual of [19683, 19539, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3144, 19680, F3, 24) (dual of [19680, 19536, 25]-code), using
(144−24, 144, 7287)-Net over F3 — Digital
Digital (120, 144, 7287)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3144, 7287, F3, 2, 24) (dual of [(7287, 2), 14430, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3144, 9841, F3, 2, 24) (dual of [(9841, 2), 19538, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3144, 19682, F3, 24) (dual of [19682, 19538, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3144, 19683, F3, 24) (dual of [19683, 19539, 25]-code), using
- 1 times truncation [i] based on linear OA(3145, 19684, F3, 25) (dual of [19684, 19539, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(3145, 19684, F3, 25) (dual of [19684, 19539, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3144, 19683, F3, 24) (dual of [19683, 19539, 25]-code), using
- OOA 2-folding [i] based on linear OA(3144, 19682, F3, 24) (dual of [19682, 19538, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(3144, 9841, F3, 2, 24) (dual of [(9841, 2), 19538, 25]-NRT-code), using
(144−24, 144, 1405344)-Net in Base 3 — Upper bound on s
There is no (120, 144, 1405345)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 507 529235 291531 140453 883465 401623 617676 504056 106925 594414 725922 149617 > 3144 [i]