MinT - Information on Result #1842069

Information on Result #1842069

(32, 53, 6555)-net in base 128, using net defined by OOA based on OOA(128⁵³, 6555, S₁₂₈, 21, 21), using

OOA 10-folding and stacking with additional row [i] based on OA(128⁵³, 65551, S₁₂₈, 21), using
- discarding factors based on OA(128⁵³, 65554, S₁₂₈, 21), using
  - discarding parts of the base [i] based on linear OA(256⁴⁶, 65554, F₂₅₆, 21) (dual of [65554, 65508, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,7]) [i] based on
      1. linear OA(256⁴¹, 65537, F₂₅₆, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(256²⁹, 65537, F₂₅₆, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
      3. linear OA(256⁵, 17, F₂₅₆, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
        discarding factors / shortening the dual code based on linear OA(256⁵, 256, F₂₅₆, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
        Reedâ€“Solomon code RS(251,256) [i]

Mode: Constructive.

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	(33, 53, 6555)-net in base 128	[i]		t-Expansion
2	(33, 54, 6555)-net in base 128	[i]		Net Duplication
3	(34, 55, 6555)-net in base 128	[i]		Net Duplication
4	(32, 52, 6555)-net in base 128	[i]		m-Reduction