MinT - Information on Result #3186219

Information on Result #3186219

Digital (165, 191, 1263)-net over F₂, using t-expansion based on digital (164, 191, 1263)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹⁹¹, 1263, F₂, 27, 27) (dual of [(1263, 27), 33910, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2¹⁹¹, 16420, F₂, 27) (dual of [16420, 16229, 28]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(2¹⁹⁰, 16419, F₂, 27) (dual of [16419, 16229, 28]-code), using
    - constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
      1. linear OA(2¹⁸³, 16384, F₂, 27) (dual of [16384, 16201, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      2. linear OA(2¹⁵⁵, 16384, F₂, 23) (dual of [16384, 16229, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(2⁷, 35, F₂, 3) (dual of [35, 28, 4]-code or 35-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: Constructive and 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 (166, 192, 1263)-net over F₂	[i]		Net Duplication
2	Digital (167, 193, 1263)-net over F₂	[i]
3	Digital (168, 194, 1263)-net over F₂	[i]