MinT - Information on Result #1021184

Information on Result #1021184

Linear OOA(3¹⁶, 157, F₃, 3, 5) (dual of [(157, 3), 455, 6]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3¹, 40, F₃, 3, 1) (dual of [(40, 3), 119, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹, s, F₃, 3, 1) for arbitrarily large s, using
  - appending 2 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, 3, 2) (dual of [(40, 3), 116, 3]-NRT-code), using
- appending 1 arbitrary column [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, 3, 5) (dual of [(77, 3), 220, 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, 2796358, F₃, 3, 11) (dual of [(2796358, 3), 8388952, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(3¹⁴⁴, 3188807, F₃, 3, 11) (dual of [(3188807, 3), 9566277, 12]-NRT-code)	[i]
3	Linear OOA(3¹⁰⁷, 2796358, F₃, 3, 10) (dual of [(2796358, 3), 8388967, 11]-NRT-code)	[i]
4	Linear OOA(3²⁴³, 5592559, F₃, 3, 16) (dual of [(5592559, 3), 16777434, 17]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs
5	Linear OOA(3²²⁷, 5592559, F₃, 3, 15) (dual of [(5592559, 3), 16777450, 16]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs