MinT - Information on Result #1846457

Information on Result #1846457

(34, 48, 131073)-net in base 32, using base change based on digital (26, 40, 131073)-net over F₆₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(64⁴⁰, 131073, F₆₄, 2, 14) (dual of [(131073, 2), 262106, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁴⁰, 262146, F₆₄, 14) (dual of [262146, 262106, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁴⁰, 262147, F₆₄, 14) (dual of [262147, 262107, 15]-code), using
    - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
      1. 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]
      2. linear OA(64³⁷, 262144, F₆₄, 13) (dual of [262144, 262107, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      3. linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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	(35, 49, 131073)-net in base 32	[i]		Net Duplication
2	(36, 50, 131073)-net in base 32	[i]		Net Duplication