MinT - Information on Result #1841203

Information on Result #1841203

(58, 83, 5462)-net in base 32, using net defined by OOA based on OOA(32⁸³, 5462, S₃₂, 25, 25), using

OOA 12-folding and stacking with additional row [i] based on OA(32⁸³, 65545, S₃₂, 25), using
- 3 times code embedding in larger space [i] based on OA(32⁸⁰, 65542, S₃₂, 25), using
  - discarding parts of the base [i] based on linear OA(256⁵⁰, 65542, F₂₅₆, 25) (dual of [65542, 65492, 26]-code), using
    - constructionÂ X applied to C([0,12]) âŠ‚ C([0,11]) [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(256⁴⁵, 65537, F₂₅₆, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [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.

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	(59, 83, 5462)-net in base 32	[i]		t-Expansion
2	(59, 84, 5462)-net in base 32	[i]		Net Duplication
3	(60, 85, 5462)-net in base 32	[i]
4	(61, 86, 5462)-net in base 32	[i]
5	(62, 87, 5462)-net in base 32	[i]
6	(58, 82, 5462)-net in base 32	[i]		m-Reduction