MinT - Information on Result #1224722

Information on Result #1224722

Digital (38, 49, 210213)-net over F₃₂, using (u,Â u+v)-construction based on

digital (2, 7, 496)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32⁷, 496, F₃₂, 5, 5) (dual of [(496, 5), 2473, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(32⁷, 993, F₃₂, 5) (dual of [993, 986, 6]-code), using
    - a code by Danev and Olsson [i]
digital (31, 42, 209717)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32⁴², 209717, F₃₂, 11, 11) (dual of [(209717, 11), 2306845, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(32⁴², 1048586, F₃₂, 11) (dual of [1048586, 1048544, 12]-code), using
    - constructionÂ X applied to C([0,5]) âŠ‚ C([0,4]) [i] based on
      1. linear OA(32⁴¹, 1048577, F₃₂, 11) (dual of [1048577, 1048536, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 32⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
      2. linear OA(32³³, 1048577, F₃₂, 9) (dual of [1048577, 1048544, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 32⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
      3. linear OA(32¹, 9, F₃₂, 1) (dual of [9, 8, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(32¹, s, F₃₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (78, 89, 6726816)-net over F₃₂	[i]		Generalized (u,Â u+v)-Construction for Nets