MinT - Information on Result #1199786

Information on Result #1199786

Digital (45, 66, 3279)-net over F₃₂, using net defined by OOA based on linear OOA(32⁶⁶, 3279, F₃₂, 21, 21) (dual of [(3279, 21), 68793, 22]-NRT-code), using

OOA 10-folding and stacking with additional row [i] based on linear OA(32⁶⁶, 32791, F₃₂, 21) (dual of [32791, 32725, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(32⁶⁶, 32792, F₃₂, 21) (dual of [32792, 32726, 22]-code), using
  - constructionÂ X applied to C([0,10]) âŠ‚ C([0,7]) [i] based on
    1. linear OA(32⁶¹, 32769, F₃₂, 21) (dual of [32769, 32708, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
    2. linear OA(32⁴³, 32769, F₃₂, 15) (dual of [32769, 32726, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
    3. linear OA(32⁵, 23, F₃₂, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,32)), using
      - discarding factors / shortening the dual code based on linear OA(32⁵, 32, F₃₂, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
        Reedâ€“Solomon code RS(27,32) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (46, 67, 3279)-net over F₃₂	[i]	Net Duplication
2	Digital (47, 68, 3279)-net over F₃₂	[i]	Net Duplication
3	Digital (45, 65, 3279)-net over F₃₂	[i]	m-Reduction