MinT - Information on Result #1185846

Information on Result #1185846

Digital (37, 44, 21852)-net over F₄, using net defined by OOA based on linear OOA(4⁴⁴, 21852, F₄, 9, 7) (dual of [(21852, 9), 196624, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(4⁴⁴, 21853, F₄, 3, 7) (dual of [(21853, 3), 65515, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(4³, 5, F₄, 3, 3) (dual of [(5, 3), 12, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;12,4) [i]
  2. linear OOA(4⁴¹, 21848, F₄, 3, 7) (dual of [(21848, 3), 65503, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(4⁴¹, 65544, F₄, 7) (dual of [65544, 65503, 8]-code), using
      - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(4⁴¹, 65536, F₄, 7) (dual of [65536, 65495, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(4³³, 65536, F₄, 6) (dual of [65536, 65503, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(4⁰, 8, F₄, 0) (dual of [8, 8, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 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		This result only	Method
1	Digital (190, 204, 4815336)-net over F₄	[i]		(u,Â u+v)-Construction for Nets
2	Digital (201, 216, 4815336)-net over F₄	[i]		(u,Â u+v)-Construction for Nets