MinT - Information on Result #1842113

Information on Result #1842113

(35, 60, 5462)-net in base 128, using net defined by OOA based on OOA(128⁶⁰, 5462, S₁₂₈, 25, 25), using

OOA 12-folding and stacking with additional row [i] based on OA(128⁶⁰, 65545, S₁₂₈, 25), using
- discarding factors based on OA(128⁶⁰, 65548, S₁₂₈, 25), using
  - discarding parts of the base [i] based on linear OA(256⁵², 65548, F₂₅₆, 25) (dual of [65548, 65496, 26]-code), using
    - constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [i] based on
      1. linear OA(256⁴⁹, 65537, F₂₅₆, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      2. 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]
      3. linear OA(256³, 11, F₂₅₆, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), using
        discarding factors / shortening the dual code based on linear OA(256³, 256, F₂₅₆, 3) (dual of [256, 253, 4]-code or 256-arc in PG(2,256) or 256-cap in PG(2,256)), using
        Reedâ€“Solomon code RS(253,256) [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	(36, 60, 5462)-net in base 128	[i]		t-Expansion
2	(36, 61, 5462)-net in base 128	[i]		Net Duplication
3	(37, 62, 5462)-net in base 128	[i]
4	(38, 63, 5462)-net in base 128	[i]
5	(35, 59, 5462)-net in base 128	[i]		m-Reduction