Best Known (146, 146+25, s)-Nets in Base 3
(146, 146+25, 4924)-Net over F3 — Constructive and digital
Digital (146, 171, 4924)-net over F3, using
- net defined by OOA [i] based on linear OOA(3171, 4924, F3, 25, 25) (dual of [(4924, 25), 122929, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3171, 59089, F3, 25) (dual of [59089, 58918, 26]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3169, 59087, F3, 25) (dual of [59087, 58918, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(3161, 59049, F3, 25) (dual of [59049, 58888, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3131, 59049, F3, 20) (dual of [59049, 58918, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(38, 38, F3, 4) (dual of [38, 30, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3169, 59087, F3, 25) (dual of [59087, 58918, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3171, 59089, F3, 25) (dual of [59089, 58918, 26]-code), using
(146, 146+25, 20919)-Net over F3 — Digital
Digital (146, 171, 20919)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3171, 20919, F3, 2, 25) (dual of [(20919, 2), 41667, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3171, 29544, F3, 2, 25) (dual of [(29544, 2), 58917, 26]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3170, 29544, F3, 2, 25) (dual of [(29544, 2), 58918, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3170, 59088, F3, 25) (dual of [59088, 58918, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3169, 59087, F3, 25) (dual of [59087, 58918, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(3161, 59049, F3, 25) (dual of [59049, 58888, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3131, 59049, F3, 20) (dual of [59049, 58918, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(38, 38, F3, 4) (dual of [38, 30, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3169, 59087, F3, 25) (dual of [59087, 58918, 26]-code), using
- OOA 2-folding [i] based on linear OA(3170, 59088, F3, 25) (dual of [59088, 58918, 26]-code), using
- 31 times duplication [i] based on linear OOA(3170, 29544, F3, 2, 25) (dual of [(29544, 2), 58918, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3171, 29544, F3, 2, 25) (dual of [(29544, 2), 58917, 26]-NRT-code), using
(146, 146+25, large)-Net in Base 3 — Upper bound on s
There is no (146, 171, large)-net in base 3, because
- 23 times m-reduction [i] would yield (146, 148, large)-net in base 3, but