MinT - Information on Result #1182506

Information on Result #1182506

Digital (228, 255, 40333)-net over F₂, using net defined by OOA based on linear OOA(2²⁵⁵, 40333, F₂, 27, 27) (dual of [(40333, 27), 1088736, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(2²⁵⁵, 524330, F₂, 27) (dual of [524330, 524075, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2²⁵⁵, 524333, F₂, 27) (dual of [524333, 524078, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
    1. linear OA(2²⁴⁸, 524288, F₂, 27) (dual of [524288, 524040, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(2²¹⁰, 524288, F₂, 23) (dual of [524288, 524078, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 524287Â = 2¹⁹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    3. linear OA(2⁷, 45, F₂, 3) (dual of [45, 38, 4]-code or 45-cap in PG(6,2)), using
      - discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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		Method
1	Digital (229, 255, 40333)-net over F₂	[i]	t-Expansion
2	Digital (229, 256, 40333)-net over F₂	[i]	Net Duplication
3	Digital (230, 257, 40333)-net over F₂	[i]
4	Digital (231, 258, 40333)-net over F₂	[i]
5	Digital (232, 259, 40333)-net over F₂	[i]
6	Digital (233, 260, 40333)-net over F₂	[i]