MinT - Information on Result #3220703

Information on Result #3220703

Digital (219, 251, 65539)-net over F₄, using t-expansion based on digital (218, 251, 65539)-net over F₄, using

net defined by OOA [i] based on linear OOA(4²⁵¹, 65539, F₄, 33, 33) (dual of [(65539, 33), 2162536, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(4²⁵¹, 1048625, F₄, 33) (dual of [1048625, 1048374, 34]-code), using
  - discarding factors / shortening the dual code based on linear OA(4²⁵¹, 1048627, F₄, 33) (dual of [1048627, 1048376, 34]-code), using
    - constructionÂ X applied to C([0,16]) âŠ‚ C([0,13]) [i] based on
      1. linear OA(4²⁴¹, 1048577, F₄, 33) (dual of [1048577, 1048336, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
      2. linear OA(4²⁰¹, 1048577, F₄, 27) (dual of [1048577, 1048376, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
      3. linear OA(4¹⁰, 50, F₄, 5) (dual of [50, 40, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹⁰, 63, F₄, 5) (dual of [63, 53, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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 (220, 252, 65539)-net over F₄	[i]		Net Duplication
2	Digital (221, 253, 65539)-net over F₄	[i]		Net Duplication