MinT - Information on Result #1170698

Information on Result #1170698

Linear OOA(2²⁹, 60, F₂, 8, 8) (dual of [(60, 8), 451, 9]-NRT-code), using appending kth column based on linear OOA(2²⁹, 60, F₂, 7, 8) (dual of [(60, 7), 391, 9]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2¹⁰, 32, F₂, 7, 4) (dual of [(32, 7), 214, 5]-NRT-code), using
  - appending 3 arbitrary columns [i] based on linear OOA(2¹⁰, 32, F₂, 4, 4) (dual of [(32, 4), 118, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹⁰, 32, F₂, 3, 4) (dual of [(32, 3), 86, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (6, 10, 32)-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(2²¹³, 1048635, F₂, 8, 16) (dual of [(1048635, 8), 8388867, 17]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²¹⁴, 1048635, F₂, 8, 17) (dual of [(1048635, 8), 8388866, 18]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Digital (21, 29, 60)-net over F₂	[i]	Net Defined by OOA