MinT - Information on Result #1215892

Information on Result #1215892

Digital (103, 129, 2549)-net over F₈, using (u,Â u+v)-construction based on

digital (5, 18, 28)-net over F₈, using
- net from sequence [i] based on digital (5, 27)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
    - a function field by SÃ©mirat [i]
digital (85, 111, 2521)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8¹¹¹, 2521, F₈, 26, 26) (dual of [(2521, 26), 65435, 27]-NRT-code), using
  - OA 13-folding and stacking [i] based on linear OA(8¹¹¹, 32773, F₈, 26) (dual of [32773, 32662, 27]-code), using
    - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
      1. linear OA(8¹¹¹, 32768, F₈, 26) (dual of [32768, 32657, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      2. linear OA(8¹⁰⁶, 32768, F₈, 25) (dual of [32768, 32662, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      3. linear OA(8⁰, 5, F₈, 0) (dual of [5, 5, 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 (104, 130, 2549)-net over F₈	[i]		Net Duplication