MinT - Information on Result #1762210

Information on Result #1762210

Digital (91, 107, 20220)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁰⁷, 20220, F₃, 2, 16) (dual of [(20220, 2), 40333, 17]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁰⁷, 29537, F₃, 2, 16) (dual of [(29537, 2), 58967, 17]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁰⁶, 29537, F₃, 2, 16) (dual of [(29537, 2), 58968, 17]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁰⁶, 59074, F₃, 16) (dual of [59074, 58968, 17]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(3¹⁰⁵, 59073, F₃, 16) (dual of [59073, 58968, 17]-code), using
      - constructionÂ X applied to C_e(15) âŠ‚ C_e(12) [i] based on
        linear OA(3¹⁰¹, 59049, F₃, 16) (dual of [59049, 58948, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
        linear OA(3⁸¹, 59049, F₃, 13) (dual of [59049, 58968, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(3⁴, 24, F₃, 2) (dual of [24, 20, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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.