MinT - Information on Result #1107233

Information on Result #1107233

Linear OOA(3¹⁶, 157, F₃, 5, 5) (dual of [(157, 5), 769, 6]-NRT-code), using appending kth column based on linear OOA(3¹⁶, 157, F₃, 4, 5) (dual of [(157, 4), 612, 6]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(3¹, 40, F₃, 4, 1) (dual of [(40, 4), 159, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3¹, s, F₃, 4, 1) for arbitrarily large s, using
    - appending 3 arbitrary columns [i] based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
2. linear OOA(3⁴, 40, F₃, 4, 2) (dual of [(40, 4), 156, 3]-NRT-code), using
  - appending 2 arbitrary columns [i] based on linear OOA(3⁴, 40, F₃, 2, 2) (dual of [(40, 2), 76, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
      - Hamming code H(4,3) [i]
3. linear OOA(3¹¹, 77, F₃, 4, 5) (dual of [(77, 4), 297, 6]-NRT-code), using
  - extracting embedded OOA [i] based on digital (6, 11, 77)-net over F₃, 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(3¹⁰⁷, 1677877, F₃, 5, 10) (dual of [(1677877, 5), 8389278, 11]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁶⁴, 4194458, F₃, 5, 10) (dual of [(4194458, 5), 20972126, 11]-NRT-code)	[i]
3	Linear OOA(3¹²², 1677877, F₃, 5, 11) (dual of [(1677877, 5), 8389263, 12]-NRT-code)	[i]
4	Linear OOA(3¹⁸⁰, 4194458, F₃, 5, 11) (dual of [(4194458, 5), 20972110, 12]-NRT-code)	[i]
5	Linear OOA(3²⁴³, 3355597, F₃, 5, 16) (dual of [(3355597, 5), 16777742, 17]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs
6	Linear OOA(3²²⁷, 3355597, F₃, 5, 15) (dual of [(3355597, 5), 16777758, 16]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs
7	Digital (11, 16, 157)-net over F₃	[i]	Net Defined by OOA