MinT - Information on Result #1707549

Information on Result #1707549

Digital (66, 74, 87388)-net over F₂, using net defined by OOA based on linear OOA(2⁷⁴, 87388, F₂, 8, 8) (dual of [(87388, 8), 699030, 9]-NRT-code), using

appending kth column [i] based on linear OOA(2⁷⁴, 87388, F₂, 7, 8) (dual of [(87388, 7), 611642, 9]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁷⁴, 87388, F₂, 3, 8) (dual of [(87388, 3), 262090, 9]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2⁷⁴, 262164, F₂, 8) (dual of [262164, 262090, 9]-code), using
    - strength reduction [i] based on linear OA(2⁷⁴, 262164, F₂, 9) (dual of [262164, 262090, 10]-code), using
      - constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
        linear OA(2⁷³, 262144, F₂, 9) (dual of [262144, 262071, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(2⁵⁵, 262144, F₂, 7) (dual of [262144, 262089, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(2¹⁹, 20, F₂, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
        dual of repetition code with length 20 [i]
        linear OA(2¹, 20, F₂, 1) (dual of [20, 19, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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

The following results depend on this result:

	Result		This result only	Method
1	Digital (67, 75, 87388)-net over F₂	[i]		Net Duplication