MinT - Information on Result #1170712

Information on Result #1170712

Linear OOA(2¹⁰⁶, 2097278, F₂, 8, 8) (dual of [(2097278, 8), 16778118, 9]-NRT-code), using appending kth column based on linear OOA(2¹⁰⁶, 2097278, F₂, 7, 8) (dual of [(2097278, 7), 14680840, 9]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2¹⁴, 128, F₂, 7, 4) (dual of [(128, 7), 882, 5]-NRT-code), using
  - appending 3 arbitrary columns [i] based on linear OOA(2¹⁴, 128, F₂, 4, 4) (dual of [(128, 4), 498, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹⁴, 128, F₂, 3, 4) (dual of [(128, 3), 370, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (10, 14, 128)-net over F₂, using
        linear code embedding found in a computer search [i]
2. linear OOA(2⁹², 2097150, F₂, 7, 8) (dual of [(2097150, 7), 14679958, 9]-NRT-code), using
  - OA 4-folding and stacking [i] based on linear OA(2⁹², 8388600, F₂, 8) (dual of [8388600, 8388508, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(2⁹², large, F₂, 8) (dual of [large, large−92, 9]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (98, 106, 2097278)-net over F₂	[i]		Net Defined by OOA