MinT - Information on Result #3190664

Information on Result #3190664

Digital (210, 236, 20166)-net over F₂, using t-expansion based on digital (209, 236, 20166)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²³⁶, 20166, F₂, 27, 27) (dual of [(20166, 27), 544246, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2²³⁶, 262159, F₂, 27) (dual of [262159, 261923, 28]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²³⁶, 262163, F₂, 27) (dual of [262163, 261927, 28]-code), using
    - constructionÂ X applied to C_e(26) âŠ‚ C_e(24) [i] based on
      1. linear OA(2²³⁵, 262144, F₂, 27) (dual of [262144, 261909, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      2. linear OA(2²¹⁷, 262144, F₂, 25) (dual of [262144, 261927, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      3. linear OA(2¹, 19, F₂, 1) (dual of [19, 18, 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 (211, 237, 20166)-net over F₂	[i]		Net Duplication
2	Digital (212, 238, 20166)-net over F₂	[i]
3	Digital (213, 239, 20166)-net over F₂	[i]