Best Known (160−24, 160, s)-Nets in Base 3
(160−24, 160, 4920)-Net over F3 — Constructive and digital
Digital (136, 160, 4920)-net over F3, using
- net defined by OOA [i] based on linear OOA(3160, 4920, F3, 24, 24) (dual of [(4920, 24), 117920, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3160, 59040, F3, 24) (dual of [59040, 58880, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3160, 59049, F3, 24) (dual of [59049, 58889, 25]-code), using
- 1 times truncation [i] based on linear OA(3161, 59050, F3, 25) (dual of [59050, 58889, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, 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(3161, 59050, F3, 25) (dual of [59050, 58889, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3160, 59049, F3, 24) (dual of [59049, 58889, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3160, 59040, F3, 24) (dual of [59040, 58880, 25]-code), using
(160−24, 160, 19683)-Net over F3 — Digital
Digital (136, 160, 19683)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3160, 19683, F3, 3, 24) (dual of [(19683, 3), 58889, 25]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3160, 59049, F3, 24) (dual of [59049, 58889, 25]-code), using
- 1 times truncation [i] based on linear OA(3161, 59050, F3, 25) (dual of [59050, 58889, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, 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(3161, 59050, F3, 25) (dual of [59050, 58889, 26]-code), using
- OOA 3-folding [i] based on linear OA(3160, 59049, F3, 24) (dual of [59049, 58889, 25]-code), using
(160−24, 160, 6080612)-Net in Base 3 — Upper bound on s
There is no (136, 160, 6080613)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 21847 472641 872107 068520 706956 490943 387397 215672 446968 411762 633614 680746 583089 > 3160 [i]