MinT - Information on Result #1107232

Information on Result #1107232

Linear OOA(3¹⁵, 117, F₃, 5, 5) (dual of [(117, 5), 570, 6]-NRT-code), using appending kth column based on linear OOA(3¹⁵, 117, F₃, 4, 5) (dual of [(117, 4), 453, 6]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. 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]
2. 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(3¹⁰⁶, 1677837, F₃, 5, 10) (dual of [(1677837, 5), 8389079, 11]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁶³, 4194418, F₃, 5, 10) (dual of [(4194418, 5), 20971927, 11]-NRT-code)	[i]
3	Linear OOA(3¹²¹, 1677837, F₃, 5, 11) (dual of [(1677837, 5), 8389064, 12]-NRT-code)	[i]
4	Linear OOA(3¹⁷⁹, 4194418, F₃, 5, 11) (dual of [(4194418, 5), 20971911, 12]-NRT-code)	[i]
5	Linear OOA(3²⁴², 3355557, F₃, 5, 16) (dual of [(3355557, 5), 16777543, 17]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs
6	Linear OOA(3²²⁶, 3355557, F₃, 5, 15) (dual of [(3355557, 5), 16777559, 16]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs
7	Digital (10, 15, 117)-net over F₃	[i]	Net Defined by OOA