Information on Result #599734
There is no digital (26, 108, 227)-net over F5, because extracting embedded orthogonal array would yield linear OA(5108, 227, F5, 82) (dual of [227, 119, 83]-code), but
- construction Y1 [i] would yield
- OA(5107, 136, S5, 82), but
- the linear programming bound shows that M ≥ 4 680614 732900 044285 630127 740921 339805 504137 246651 693367 478774 820966 691549 983806 908130 645751 953125 / 7377 156347 408094 956731 > 5107 [i]
- linear OA(5119, 227, F5, 91) (dual of [227, 108, 92]-code), but
- discarding factors / shortening the dual code would yield linear OA(5119, 214, F5, 91) (dual of [214, 95, 92]-code), but
- construction Y1 [i] would yield
- OA(5118, 142, S5, 91), but
- the linear programming bound shows that M ≥ 227 290310 028755 622094 163273 225192 363202 339181 888847 417767 861303 072862 710905 610583 722591 400146 484375 / 5712 266942 976429 > 5118 [i]
- OA(595, 214, S5, 72), but
- discarding factors would yield OA(595, 145, S5, 72), but
- the linear programming bound shows that M ≥ 681 594308 011084 642541 521008 533375 736738 792368 662881 901785 086204 561152 741164 839513 298410 490771 406244 903118 931688 368320 465087 890625 / 251 826768 360176 313961 784872 463983 728554 549094 621216 187309 311959 > 595 [i]
- discarding factors would yield OA(595, 145, S5, 72), but
- OA(5118, 142, S5, 91), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(5119, 214, F5, 91) (dual of [214, 95, 92]-code), but
- OA(5107, 136, S5, 82), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.