MinT - Information on Result #1756468

Information on Result #1756468

Digital (189, 216, 10929)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²¹⁶, 10929, F₂, 6, 27) (dual of [(10929, 6), 65358, 28]-NRT-code), using

OOA 6-folding [i] based on linear OA(2²¹⁶, 65574, F₂, 27) (dual of [65574, 65358, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2²¹⁶, 65575, F₂, 27) (dual of [65575, 65359, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
    1. linear OA(2²⁰⁹, 65536, F₂, 27) (dual of [65536, 65327, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(2¹⁷⁷, 65536, F₂, 23) (dual of [65536, 65359, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    3. linear OA(2⁷, 39, F₂, 3) (dual of [39, 32, 4]-code or 39-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 (190, 217, 10929)-net over F₂	[i]		Net Duplication
2	Digital (191, 218, 10929)-net over F₂	[i]
3	Digital (192, 219, 10929)-net over F₂	[i]
4	Digital (193, 220, 10929)-net over F₂	[i]