MinT - Information on Result #1191034

Information on Result #1191034

Digital (26, 32, 174764)-net over F₈, using net defined by OOA based on linear OOA(8³², 174764, F₈, 6, 6) (dual of [(174764, 6), 1048552, 7]-NRT-code), using

OA 3-folding and stacking [i] based on linear OA(8³², 524292, F₈, 6) (dual of [524292, 524260, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(8³², 524294, F₈, 6) (dual of [524294, 524262, 7]-code), using
  - trace code [i] based on linear OA(64¹⁶, 262147, F₆₄, 6) (dual of [262147, 262131, 7]-code), using
    - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
      1. linear OA(64¹⁶, 262144, F₆₄, 6) (dual of [262144, 262128, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
      2. linear OA(64¹³, 262144, F₆₄, 5) (dual of [262144, 262131, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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: 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

The following results depend on this result:

	Result		Method
1	Digital (29, 35, 174773)-net over F₈	[i]	(u,Â u+v)-Construction for Nets
2	Digital (110, 122, 2970964)-net over F₈	[i]
3	Digital (117, 130, 2970964)-net over F₈	[i]