MinT - Information on Result #1846617

Information on Result #1846617

(9, 16, 32771)-net in base 128, using base change based on digital (7, 14, 32771)-net over F₂₅₆, using

net defined by OOA [i] based on linear OOA(256¹⁴, 32771, F₂₅₆, 7, 7) (dual of [(32771, 7), 229383, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(256¹⁴, 32771, F₂₅₆, 6, 7) (dual of [(32771, 6), 196612, 8]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(256¹⁴, 32771, F₂₅₆, 2, 7) (dual of [(32771, 2), 65528, 8]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(256¹⁴, 65542, F₂₅₆, 7) (dual of [65542, 65528, 8]-code), using
      - constructionÂ X applied to C([0,3]) âŠ‚ C([0,2]) [i] based on
        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]
        linear OA(256⁹, 65537, F₂₅₆, 5) (dual of [65537, 65528, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
        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: Arbitrary.

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	OOA(128¹⁶, 32771, S₁₂₈, 3, 7)	[i]		Extracting Embedded OOA
2	OOA(128¹⁶, 32771, S₁₂₈, 4, 7)	[i]		Extracting Embedded OOA