MinT - Information on Result #1825346

Information on Result #1825346

(49, 63, 37450)-net in base 16, using base change based on digital (28, 42, 37450)-net over F₆₄, using

64¹ times duplication [i] based on digital (27, 41, 37450)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64⁴¹, 37450, F₆₄, 14, 14) (dual of [(37450, 14), 524259, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(64⁴¹, 262150, F₆₄, 14) (dual of [262150, 262109, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(64⁴¹, 262151, F₆₄, 14) (dual of [262151, 262110, 15]-code), using
      - constructionÂ X applied to C_e(13) âŠ‚ C_e(11) [i] based on
        linear OA(64⁴⁰, 262144, F₆₄, 14) (dual of [262144, 262104, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(64³⁴, 262144, F₆₄, 12) (dual of [262144, 262110, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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	(50, 64, 37450)-net in base 16	[i]		Net Duplication