MinT - Information on Result #906190

Information on Result #906190

Linear OOA(3¹⁸, 285, F₃, 2, 5) (dual of [(285, 2), 552, 6]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3¹, 95, F₃, 2, 1) (dual of [(95, 2), 189, 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, 95, F₃, 2, 2) (dual of [(95, 2), 185, 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(3¹², 95, F₃, 2, 5) (dual of [(95, 2), 178, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 12, 95)-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(3¹²⁴, 4194586, F₃, 2, 11) (dual of [(4194586, 2), 8389048, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁰⁹, 4194586, F₃, 2, 10) (dual of [(4194586, 2), 8389063, 11]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(3¹⁸, 284, F₃, 3, 5) (dual of [(284, 3), 834, 6]-NRT-code)	[i]	OOA Stacking with Additional Row
4	Linear OOA(3¹⁸, 284, F₃, 4, 5) (dual of [(284, 4), 1118, 6]-NRT-code)	[i]
5	Linear OOA(3¹⁸, 284, F₃, 5, 5) (dual of [(284, 5), 1402, 6]-NRT-code)	[i]