MinT - Information on Result #1170697

Information on Result #1170697

Linear OOA(2²⁸, 53, F₂, 8, 8) (dual of [(53, 8), 396, 9]-NRT-code), using appending kth column based on linear OOA(2²⁸, 53, F₂, 7, 8) (dual of [(53, 7), 343, 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(2¹⁹, 30, F₂, 7, 8) (dual of [(30, 7), 191, 9]-NRT-code), using
  - extracting embedded OOA [i] based on digital (11, 19, 30)-net over F₂, using
    - linear code embedding found in a computer search [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2²¹², 1048628, F₂, 8, 16) (dual of [(1048628, 8), 8388812, 17]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²¹³, 1048628, F₂, 8, 17) (dual of [(1048628, 8), 8388811, 18]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Digital (20, 28, 53)-net over F₂	[i]	Net Defined by OOA