MinT - Information on Result #3187593

Information on Result #3187593

Digital (182, 206, 10924)-net over F₂, using t-expansion based on digital (181, 206, 10924)-net over F₂, using

net defined by OOA [i] based on linear OOA(2²⁰⁶, 10924, F₂, 25, 25) (dual of [(10924, 25), 272894, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2²⁰⁶, 131089, F₂, 25) (dual of [131089, 130883, 26]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁰⁶, 131090, F₂, 25) (dual of [131090, 130884, 26]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(22) [i] based on
      1. linear OA(2²⁰⁵, 131072, F₂, 25) (dual of [131072, 130867, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      2. linear OA(2¹⁸⁸, 131072, F₂, 23) (dual of [131072, 130884, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(2¹, 18, F₂, 1) (dual of [18, 17, 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 (183, 207, 10924)-net over F₂	[i]		Net Duplication
2	Digital (184, 208, 10924)-net over F₂	[i]
3	Digital (185, 209, 10924)-net over F₂	[i]