MinT - Information on Result #3193587

Information on Result #3193587

Digital (245, 259, 2398786)-net over F₂, using t-expansion based on digital (244, 259, 2398786)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (58, 65, 2097150)-net over F₂, using
  - net defined by OOA [i] based on linear OOA(2⁶⁵, 2097150, F₂, 7, 7) (dual of [(2097150, 7), 14679985, 8]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
      - OOAs constructed from BCH codes [i]
2. digital (179, 194, 1199393)-net over F₂, using
  - (u,Â u+v)-construction [i] based on
    1. digital (25, 32, 1022)-net over F₂, using
      - net defined by OOA [i] based on linear OOA(2³², 1022, F₂, 7, 7) (dual of [(1022, 7), 7122, 8]-NRT-code), using
        OOA stacking with additional row [i] based on linear OOA(2³², 1023, F₂, 3, 7) (dual of [(1023, 3), 3037, 8]-NRT-code), using
        OOAs constructed from BCH codes [i]
    2. digital (147, 162, 1198371)-net over F₂, using
      - net defined by OOA [i] based on linear OOA(2¹⁶², 1198371, F₂, 15, 15) (dual of [(1198371, 15), 17975403, 16]-NRT-code), using
        OOA 7-folding and stacking with additional row [i] based on linear OA(2¹⁶², 8388598, F₂, 15) (dual of [8388598, 8388436, 16]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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 (246, 260, 2398786)-net over F₂	[i]		Net Duplication