MinT - Information on Result #1170723

Information on Result #1170723

Linear OOA(2¹²³, 4194318, F₂, 8, 8) (dual of [(4194318, 8), 33554421, 9]-NRT-code), using appending kth column based on linear OOA(2¹²³, 4194318, F₂, 7, 8) (dual of [(4194318, 7), 29360103, 9]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁸, 17, F₂, 7, 4) (dual of [(17, 7), 111, 5]-NRT-code), using
  - appending 3 arbitrary columns [i] based on linear OOA(2⁸, 17, F₂, 4, 4) (dual of [(17, 4), 60, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(2⁸, 17, F₂, 3, 4) (dual of [(17, 3), 43, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (4, 8, 17)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
2. linear OOA(2¹¹⁵, 4194301, F₂, 7, 8) (dual of [(4194301, 7), 29359992, 9]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OOA(2¹¹⁵, large, F₂, 2, 8), using
    - OOAs constructed from BCH codes [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 (115, 123, 4194318)-net over F₂	[i]		Net Defined by OOA