MinT - Information on Result #3243755

Information on Result #3243755

Digital (66, 96, 2186)-net over F₃₂, using t-expansion based on digital (65, 96, 2186)-net over F₃₂, using

net defined by OOA [i] based on linear OOA(32⁹⁶, 2186, F₃₂, 31, 31) (dual of [(2186, 31), 67670, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(32⁹⁶, 32791, F₃₂, 31) (dual of [32791, 32695, 32]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁹⁶, 32792, F₃₂, 31) (dual of [32792, 32696, 32]-code), using
    - constructionÂ X applied to C([0,15]) âŠ‚ C([0,12]) [i] based on
      1. linear OA(32⁹¹, 32769, F₃₂, 31) (dual of [32769, 32678, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
      2. linear OA(32⁷³, 32769, F₃₂, 25) (dual of [32769, 32696, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769Â | 32⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (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		This result only	Method
1	Digital (67, 97, 2186)-net over F₃₂	[i]		Net Duplication