MinT - Information on Result #1842165

Information on Result #1842165

(45, 76, 4370)-net in base 128, using net defined by OOA based on OOA(128⁷⁶, 4370, S₁₂₈, 31, 31), using

OOA 15-folding and stacking with additional row [i] based on OA(128⁷⁶, 65551, S₁₂₈, 31), using
- discarding factors based on OA(128⁷⁶, 65554, S₁₂₈, 31), using
  - discarding parts of the base [i] based on linear OA(256⁶⁶, 65554, F₂₅₆, 31) (dual of [65554, 65488, 32]-code), using
    - constructionÂ X applied to C([0,15]) âŠ‚ C([0,12]) [i] based on
      1. linear OA(256⁶¹, 65537, F₂₅₆, 31) (dual of [65537, 65476, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
      2. 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]
      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	(46, 76, 4370)-net in base 128	[i]		t-Expansion
2	(46, 77, 4370)-net in base 128	[i]		Net Duplication
3	(47, 78, 4370)-net in base 128	[i]		Net Duplication
4	(45, 75, 4370)-net in base 128	[i]		m-Reduction