MinT - Information on Result #1178855

Information on Result #1178855

Digital (57, 65, 16388)-net over F₂, using net defined by OOA based on linear OOA(2⁶⁵, 16388, F₂, 8, 8) (dual of [(16388, 8), 131039, 9]-NRT-code), using

OA 4-folding and stacking [i] based on linear OA(2⁶⁵, 65552, F₂, 8) (dual of [65552, 65487, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2⁶⁵, 65553, F₂, 8) (dual of [65553, 65488, 9]-code), using
  - 1 times truncation [i] based on linear OA(2⁶⁶, 65554, F₂, 9) (dual of [65554, 65488, 10]-code), using
    - constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
      1. linear OA(2⁶⁵, 65536, F₂, 9) (dual of [65536, 65471, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(2⁴⁹, 65536, F₂, 7) (dual of [65536, 65487, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(2¹⁷, 18, F₂, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
        dual of repetition code with length 18 [i]
      4. 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 (233, 249, 1064963)-net over F₂	[i]		(u,Â u+v)-Construction for Nets
2	Digital (233, 250, 1064963)-net over F₂	[i]		(u,Â u+v)-Construction for Nets