MinT - Information on Result #3185086

Information on Result #3185086

Digital (156, 178, 5959)-net over F₂, using t-expansion based on digital (155, 178, 5959)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹⁷⁸, 5959, F₂, 23, 23) (dual of [(5959, 23), 136879, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2¹⁷⁸, 65550, F₂, 23) (dual of [65550, 65372, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁷⁸, 65553, F₂, 23) (dual of [65553, 65375, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(20) [i] based on
      1. 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]
      2. linear OA(2¹⁶¹, 65536, F₂, 21) (dual of [65536, 65375, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. linear OA(2¹, 17, F₂, 1) (dual of [17, 16, 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: 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 (157, 179, 5959)-net over F₂	[i]		Net Duplication
2	Digital (158, 180, 5959)-net over F₂	[i]
3	Digital (159, 181, 5959)-net over F₂	[i]