MinT - Information on Result #1766295

Information on Result #1766295

Digital (162, 179, 3255381)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁷⁹, 3255381, F₃, 2, 17) (dual of [(3255381, 2), 6510583, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁷⁹, 4194318, F₃, 2, 17) (dual of [(4194318, 2), 8388457, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹³, 17, F₃, 2, 8) (dual of [(17, 2), 21, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (5, 13, 17)-net over F₃, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(3¹⁶⁶, 4194301, F₃, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹⁶⁶, 8388602, F₃, 17) (dual of [8388602, 8388436, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁶⁶, large, F₃, 17) (dual of [large, large−166, 18]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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.