MinT - Information on Result #1824176

Information on Result #1824176

(39, 54, 37450)-net in base 32, using base change based on digital (30, 45, 37450)-net over F₆₄, using

64¹ times duplication [i] based on digital (29, 44, 37450)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64⁴⁴, 37450, F₆₄, 15, 15) (dual of [(37450, 15), 561706, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(64⁴⁴, 262151, F₆₄, 15) (dual of [262151, 262107, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(64⁴⁴, 262152, F₆₄, 15) (dual of [262152, 262108, 16]-code), using
      - constructionÂ X applied to C([0,7]) âŠ‚ C([0,6]) [i] based on
        linear OA(64⁴³, 262145, F₆₄, 15) (dual of [262145, 262102, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
        linear OA(64³⁷, 262145, F₆₄, 13) (dual of [262145, 262108, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145Â | 64⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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.

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	(40, 55, 37450)-net in base 32	[i]		Net Duplication