MinT - Information on Result #3182258

Information on Result #3182258

Digital (122, 138, 16386)-net over F₂, using t-expansion based on digital (121, 138, 16386)-net over F₂, using

net defined by OOA [i] based on linear OOA(2¹³⁸, 16386, F₂, 17, 17) (dual of [(16386, 17), 278424, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2¹³⁸, 131089, F₂, 17) (dual of [131089, 130951, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹³⁸, 131090, F₂, 17) (dual of [131090, 130952, 18]-code), using
    - constructionÂ X applied to C_e(16) âŠ‚ C_e(14) [i] based on
      1. linear OA(2¹³⁷, 131072, F₂, 17) (dual of [131072, 130935, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
      2. linear OA(2¹²⁰, 131072, F₂, 15) (dual of [131072, 130952, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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 (123, 139, 16386)-net over F₂	[i]		Net Duplication
2	Digital (124, 140, 16386)-net over F₂	[i]
3	Digital (125, 141, 16386)-net over F₂	[i]