MinT - Information on Result #1084720

Information on Result #1084720

Linear OOA(3¹⁶, 157, F₃, 4, 5) (dual of [(157, 4), 612, 6]-NRT-code), using generalized (u,Â u+v)-construction based on

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]
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]
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.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(3¹²², 2097307, F₃, 4, 11) (dual of [(2097307, 4), 8389106, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁴⁴, 2391645, F₃, 4, 11) (dual of [(2391645, 4), 9566436, 12]-NRT-code)	[i]
3	Linear OOA(3¹⁰⁷, 2097307, F₃, 4, 10) (dual of [(2097307, 4), 8389121, 11]-NRT-code)	[i]
4	Linear OOA(3²⁴³, 4194457, F₃, 4, 16) (dual of [(4194457, 4), 16777585, 17]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs
5	Linear OOA(3²²⁷, 4194457, F₃, 4, 15) (dual of [(4194457, 4), 16777601, 16]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs
6	Linear OOA(3¹⁶, 157, F₃, 5, 5) (dual of [(157, 5), 769, 6]-NRT-code)	[i]	Appending kth Column