MinT - Information on Result #1191124

Information on Result #1191124

Digital (39, 46, 699061)-net over F₈, using net defined by OOA based on linear OOA(8⁴⁶, 699061, F₈, 9, 7) (dual of [(699061, 9), 6291503, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(8⁴⁶, 699062, F₈, 3, 7) (dual of [(699062, 3), 2097140, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8³, 9, F₈, 3, 3) (dual of [(9, 3), 24, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;24,8) [i]
  2. linear OOA(8⁴³, 699053, F₈, 3, 7) (dual of [(699053, 3), 2097116, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(8⁴³, 2097159, F₈, 7) (dual of [2097159, 2097116, 8]-code), using
      - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(8⁴³, 2097152, F₈, 7) (dual of [2097152, 2097109, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(8³⁶, 2097152, F₈, 6) (dual of [2097152, 2097116, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(8⁰, 7, F₈, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 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 (138, 152, 3095803)-net over F₈	[i]		(u,Â u+v)-Construction for Nets
2	Digital (145, 160, 3095803)-net over F₈	[i]		(u,Â u+v)-Construction for Nets