MinT - Information on Result #1226862

Information on Result #1226862

Digital (28, 39, 54446)-net over F₆₄, using (u,Â u+v)-construction based on

digital (2, 7, 2016)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64⁷, 2016, F₆₄, 5, 5) (dual of [(2016, 5), 10073, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
    - a code by Danev and Olsson [i]
digital (21, 32, 52430)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64³², 52430, F₆₄, 11, 11) (dual of [(52430, 11), 576698, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(64³², 262151, F₆₄, 11) (dual of [262151, 262119, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(64³², 262152, F₆₄, 11) (dual of [262152, 262120, 12]-code), using
      - constructionÂ X applied to C([0,5]) âŠ‚ C([0,4]) [i] based on
        linear OA(64³¹, 262145, F₆₄, 11) (dual of [262145, 262114, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
        linear OA(64²⁵, 262145, F₆₄, 9) (dual of [262145, 262120, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
        linear OA(64¹, 7, F₆₄, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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

None.