MinT - Information on Result #1194870

Information on Result #1194870

Digital (24, 32, 32770)-net over F₁₆, using net defined by OOA based on linear OOA(16³², 32770, F₁₆, 8, 8) (dual of [(32770, 8), 262128, 9]-NRT-code), using

OA 4-folding and stacking [i] based on linear OA(16³², 131080, F₁₆, 8) (dual of [131080, 131048, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(16³², 131082, F₁₆, 8) (dual of [131082, 131050, 9]-code), using
  - trace code [i] based on linear OA(256¹⁶, 65541, F₂₅₆, 8) (dual of [65541, 65525, 9]-code), using
    - constructionÂ X applied to C_e(7) âŠ‚ C_e(5) [i] based on
      1. linear OA(256¹⁵, 65536, F₂₅₆, 8) (dual of [65536, 65521, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
      2. linear OA(256¹¹, 65536, F₂₅₆, 6) (dual of [65536, 65525, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      3. linear OA(256¹, 5, F₂₅₆, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 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		Method
1	Digital (25, 33, 32770)-net over F₁₆	[i]	Net Duplication
2	Digital (108, 124, 2129920)-net over F₁₆	[i]	(u,Â u+v)-Construction for Nets
3	Digital (113, 130, 2129920)-net over F₁₆	[i]	(u,Â u+v)-Construction for Nets