Best Known (181, 181+30, s)-Nets in Base 3
(181, 181+30, 3940)-Net over F3 — Constructive and digital
Digital (181, 211, 3940)-net over F3, using
- net defined by OOA [i] based on linear OOA(3211, 3940, F3, 30, 30) (dual of [(3940, 30), 117989, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3211, 59100, F3, 30) (dual of [59100, 58889, 31]-code), using
- 1 times truncation [i] based on linear OA(3212, 59101, F3, 31) (dual of [59101, 58889, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- linear OA(3201, 59050, F3, 31) (dual of [59050, 58849, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 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]
- linear OA(311, 51, F3, 5) (dual of [51, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- 1 times truncation [i] based on linear OA(3212, 59101, F3, 31) (dual of [59101, 58889, 32]-code), using
- OA 15-folding and stacking [i] based on linear OA(3211, 59100, F3, 30) (dual of [59100, 58889, 31]-code), using
(181, 181+30, 26930)-Net over F3 — Digital
Digital (181, 211, 26930)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3211, 26930, F3, 2, 30) (dual of [(26930, 2), 53649, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3211, 29550, F3, 2, 30) (dual of [(29550, 2), 58889, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3211, 59100, F3, 30) (dual of [59100, 58889, 31]-code), using
- 1 times truncation [i] based on linear OA(3212, 59101, F3, 31) (dual of [59101, 58889, 32]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- linear OA(3201, 59050, F3, 31) (dual of [59050, 58849, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 320−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- 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]
- linear OA(311, 51, F3, 5) (dual of [51, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to C([0,15]) ⊂ C([0,12]) [i] based on
- 1 times truncation [i] based on linear OA(3212, 59101, F3, 31) (dual of [59101, 58889, 32]-code), using
- OOA 2-folding [i] based on linear OA(3211, 59100, F3, 30) (dual of [59100, 58889, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(3211, 29550, F3, 2, 30) (dual of [(29550, 2), 58889, 31]-NRT-code), using
(181, 181+30, large)-Net in Base 3 — Upper bound on s
There is no (181, 211, large)-net in base 3, because
- 28 times m-reduction [i] would yield (181, 183, large)-net in base 3, but