MinT - Information on Result #1186744

Information on Result #1186744

Digital (113, 131, 116509)-net over F₄, using net defined by OOA based on linear OOA(4¹³¹, 116509, F₄, 18, 18) (dual of [(116509, 18), 2097031, 19]-NRT-code), using

OA 9-folding and stacking [i] based on linear OA(4¹³¹, 1048581, F₄, 18) (dual of [1048581, 1048450, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹³¹, 1048586, F₄, 18) (dual of [1048586, 1048455, 19]-code), using
  - constructionÂ X applied to C_e(17) âŠ‚ C_e(16) [i] based on
    1. linear OA(4¹³¹, 1048576, F₄, 18) (dual of [1048576, 1048445, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    2. linear OA(4¹²¹, 1048576, F₄, 17) (dual of [1048576, 1048455, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
    3. linear OA(4⁰, 10, F₄, 0) (dual of [10, 10, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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 (114, 132, 116509)-net over F₄	[i]	Net Duplication
2	Digital (115, 133, 116509)-net over F₄	[i]	Net Duplication
3	Digital (122, 140, 116514)-net over F₄	[i]	(u,Â u+v)-Construction for Nets
4	Digital (123, 141, 116518)-net over F₄	[i]
5	Digital (124, 142, 116519)-net over F₄	[i]
6	Digital (125, 143, 116523)-net over F₄	[i]