MinT - Information on Result #1208692

Information on Result #1208692

Digital (171, 194, 48321)-net over F₃, using (u,Â u+v)-construction based on

digital (2, 13, 8)-net over F₃, using
- net from sequence [i] based on digital (2, 7)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 2 and N(F) ≥ 8, using
    - an explicitly constructive algebraic function field [i]
digital (158, 181, 48313)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3¹⁸¹, 48313, F₃, 23, 23) (dual of [(48313, 23), 1111018, 24]-NRT-code), using
  - OOA 11-folding and stacking with additional row [i] based on linear OA(3¹⁸¹, 531444, F₃, 23) (dual of [531444, 531263, 24]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁸¹, 531453, F₃, 23) (dual of [531453, 531272, 24]-code), using
      - constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
        linear OA(3¹⁸¹, 531441, F₃, 23) (dual of [531441, 531260, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
        linear OA(3¹⁶⁹, 531441, F₃, 22) (dual of [531441, 531272, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(3⁰, 12, F₃, 0) (dual of [12, 12, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 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

None.