MinT - Information on Result #906189

Information on Result #906189

Linear OOA(3¹⁷, 231, F₃, 2, 5) (dual of [(231, 2), 445, 6]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3¹, 77, F₃, 2, 1) (dual of [(77, 2), 153, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹, s, F₃, 2, 1) for arbitrarily large s, using
  - appending 1 arbitrary column [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(3⁵, 77, F₃, 2, 2) (dual of [(77, 2), 149, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁵, 121, F₃, 2, 2) (dual of [(121, 2), 237, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(3⁵, 121, F₃, 2) (dual of [121, 116, 3]-code), using
    - Hamming code H(5,3) [i]
linear OOA(3¹¹, 77, F₃, 2, 5) (dual of [(77, 2), 143, 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(3¹²³, 4194532, F₃, 2, 11) (dual of [(4194532, 2), 8388941, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁴⁵, 4783207, F₃, 2, 11) (dual of [(4783207, 2), 9566269, 12]-NRT-code)	[i]
3	Linear OOA(3¹⁰⁸, 4194532, F₃, 2, 10) (dual of [(4194532, 2), 8388956, 11]-NRT-code)	[i]
4	Linear OOA(3¹⁷, 230, F₃, 3, 5) (dual of [(230, 3), 673, 6]-NRT-code)	[i]	OOA Stacking with Additional Row
5	Linear OOA(3¹⁷, 230, F₃, 4, 5) (dual of [(230, 4), 903, 6]-NRT-code)	[i]
6	Linear OOA(3¹⁷, 230, F₃, 5, 5) (dual of [(230, 5), 1133, 6]-NRT-code)	[i]