MinT - Information on Result #1179240

Information on Result #1179240

Digital (100, 109, 2097407)-net over F₂, using net defined by OOA based on linear OOA(2¹⁰⁹, 2097407, F₂, 9, 9) (dual of [(2097407, 9), 18876554, 10]-NRT-code), using

appending kth column [i] based on linear OOA(2¹⁰⁹, 2097407, F₂, 8, 9) (dual of [(2097407, 8), 16779147, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁶, 257, F₂, 8, 4) (dual of [(257, 8), 2040, 5]-NRT-code), using
    - appending 4 arbitrary columns [i] based on linear OOA(2¹⁶, 257, F₂, 4, 4) (dual of [(257, 4), 1012, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(2¹⁶, 257, F₂, 3, 4) (dual of [(257, 3), 755, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (12, 16, 257)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
  2. linear OOA(2⁹³, 2097150, F₂, 8, 9) (dual of [(2097150, 8), 16777107, 10]-NRT-code), using
    - OOA 4-folding and stacking with additional row [i] based on linear OA(2⁹³, 8388601, F₂, 9) (dual of [8388601, 8388508, 10]-code), using
      - discarding factors / shortening the dual code based on linear OA(2⁹³, large, F₂, 9) (dual of [large, large−93, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [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 (101, 109, 2097407)-net over F₂	[i]		t-Expansion
2	Digital (101, 110, 2097407)-net over F₂	[i]		Net Duplication