MinT - Information on Result #1170724

Information on Result #1170724

Linear OOA(2¹²⁴, 4194324, F₂, 8, 8) (dual of [(4194324, 8), 33554468, 9]-NRT-code), using appending kth column based on linear OOA(2¹²⁴, 4194324, F₂, 7, 8) (dual of [(4194324, 7), 29360144, 9]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁹, 23, F₂, 7, 4) (dual of [(23, 7), 152, 5]-NRT-code), using
  - appending 3 arbitrary columns [i] based on linear OOA(2⁹, 23, F₂, 4, 4) (dual of [(23, 4), 83, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(2⁹, 23, F₂, 3, 4) (dual of [(23, 3), 60, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (5, 9, 23)-net over F₂, using
        linear code embedding found in a computer search [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 (116, 124, 4194324)-net over F₂	[i]		Net Defined by OOA