MinT - Information on Result #1764500

Information on Result #1764500

Digital (133, 152, 176241)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁵², 176241, F₃, 3, 19) (dual of [(176241, 3), 528571, 20]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁵², 177157, F₃, 3, 19) (dual of [(177157, 3), 531319, 20]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁵¹, 177157, F₃, 3, 19) (dual of [(177157, 3), 531320, 20]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁵¹, 531471, F₃, 19) (dual of [531471, 531320, 20]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁵¹, 531472, F₃, 19) (dual of [531472, 531321, 20]-code), using
      - constructionÂ X applied to C([0,9]) âŠ‚ C([0,7]) [i] based on
        linear OA(3¹⁴⁵, 531442, F₃, 19) (dual of [531442, 531297, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
        linear OA(3¹²¹, 531442, F₃, 15) (dual of [531442, 531321, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
        linear OA(3⁶, 30, F₃, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,3)), using
        discarding factors / shortening the dual code based on linear OA(3⁶, 48, F₃, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
        large caps in PG(5,Â b) [i]

Mode: 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.