MinT - Information on Result #1756628

Information on Result #1756628

Digital (196, 218, 87389)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹⁸, 87389, F₂, 6, 22) (dual of [(87389, 6), 524116, 23]-NRT-code), using

OOA 6-folding [i] based on linear OA(2²¹⁸, 524334, F₂, 22) (dual of [524334, 524116, 23]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2²¹⁶, 524332, F₂, 22) (dual of [524332, 524116, 23]-code), using
  - 1 times truncation [i] based on linear OA(2²¹⁷, 524333, F₂, 23) (dual of [524333, 524116, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
      1. linear OA(2²¹⁰, 524288, F₂, 23) (dual of [524288, 524078, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(2¹⁷², 524288, F₂, 19) (dual of [524288, 524116, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(2⁷, 45, F₂, 3) (dual of [45, 38, 4]-code or 45-cap in PG(6,2)), using
        discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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 (197, 219, 87389)-net over F₂	[i]		Net Duplication