MinT - Information on Result #1841255

Information on Result #1841255

(68, 97, 4682)-net in base 32, using net defined by OOA based on OOA(32⁹⁷, 4682, S₃₂, 29, 29), using

OOA 14-folding and stacking with additional row [i] based on OA(32⁹⁷, 65549, S₃₂, 29), using
- 1 times code embedding in larger space [i] based on OA(32⁹⁶, 65548, S₃₂, 29), using
  - discarding parts of the base [i] based on linear OA(256⁶⁰, 65548, F₂₅₆, 29) (dual of [65548, 65488, 30]-code), using
    - constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
      1. linear OA(256⁵⁷, 65537, F₂₅₆, 29) (dual of [65537, 65480, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (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(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	(69, 97, 4682)-net in base 32	[i]		t-Expansion
2	(69, 98, 4682)-net in base 32	[i]		Net Duplication
3	(70, 99, 4682)-net in base 32	[i]
4	(71, 100, 4682)-net in base 32	[i]
5	(72, 101, 4682)-net in base 32	[i]