MinT - Information on Result #1204418

Information on Result #1204418

Digital (13, 24, 13109)-net over F₂₅₆, using net defined by OOA based on linear OOA(256²⁴, 13109, F₂₅₆, 11, 11) (dual of [(13109, 11), 144175, 12]-NRT-code), using

OOA 5-folding and stacking with additional row [i] based on linear OA(256²⁴, 65546, F₂₅₆, 11) (dual of [65546, 65522, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(256²⁴, 65548, F₂₅₆, 11) (dual of [65548, 65524, 12]-code), using
  - constructionÂ X applied to C([0,5]) âŠ‚ C([0,3]) [i] based on
    1. linear OA(256²¹, 65537, F₂₅₆, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
    2. linear OA(256¹³, 65537, F₂₅₆, 7) (dual of [65537, 65524, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (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 and linear.

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	Digital (14, 25, 13109)-net over F₂₅₆	[i]		Net Duplication
2	Digital (36, 47, 3355904)-net over F₂₅₆	[i]		Generalized (u,Â u+v)-Construction for Nets