MinT - Information on Result #1170700

Information on Result #1170700

Linear OOA(2³¹, 71, F₂, 8, 8) (dual of [(71, 8), 537, 9]-NRT-code), using appending kth column based on linear OOA(2³¹, 71, F₂, 7, 8) (dual of [(71, 7), 466, 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(2²¹, 39, F₂, 7, 8) (dual of [(39, 7), 252, 9]-NRT-code), using
  - extracting embedded OOA [i] based on digital (13, 21, 39)-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(2²¹⁵, 1048646, F₂, 8, 16) (dual of [(1048646, 8), 8388953, 17]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²¹⁶, 1048646, F₂, 8, 17) (dual of [(1048646, 8), 8388952, 18]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Digital (23, 31, 71)-net over F₂	[i]	Net Defined by OOA