MinT - Information on Result #1764102

Information on Result #1764102

Digital (128, 145, 461314)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁴⁵, 461314, F₃, 3, 17) (dual of [(461314, 3), 1383797, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁴⁵, 531445, F₃, 3, 17) (dual of [(531445, 3), 1594190, 18]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3¹⁴⁴, 531445, F₃, 3, 17) (dual of [(531445, 3), 1594191, 18]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(3¹⁴⁴, 1594335, F₃, 17) (dual of [1594335, 1594191, 18]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁴⁴, 1594336, F₃, 17) (dual of [1594336, 1594192, 18]-code), using
      - constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
        linear OA(3¹⁴⁴, 1594323, F₃, 17) (dual of [1594323, 1594179, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(3¹³¹, 1594323, F₃, 16) (dual of [1594323, 1594192, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
        linear OA(3⁰, 13, F₃, 0) (dual of [13, 13, 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: 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.