Information on Result #599743
There is no digital (29, 122, 230)-net over F5, because extracting embedded orthogonal array would yield linear OA(5122, 230, F5, 93) (dual of [230, 108, 94]-code), but
- construction Y1 [i] would yield
- OA(5121, 148, S5, 93), but
- the linear programming bound shows that M ≥ 32369 614861 849619 401750 006027 906460 896693 183159 168094 972472 912293 146030 116020 028799 539431 929588 317871 093750 / 5704 050953 652436 468413 > 5121 [i]
- linear OA(5108, 230, F5, 82) (dual of [230, 122, 83]-code), but
- discarding factors / shortening the dual code would yield linear OA(5108, 228, F5, 82) (dual of [228, 120, 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]
- OA(5120, 228, S5, 92), but
- discarding factors would yield OA(5120, 149, S5, 92), but
- the linear programming bound shows that M ≥ 1875 115433 709844 937609 244603 657370 223629 726878 856922 329955 321895 357533 978909 714278 415776 789188 385009 765625 / 2299 458852 249280 370649 > 5120 [i]
- discarding factors would yield OA(5120, 149, S5, 92), but
- OA(5107, 136, S5, 82), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(5108, 228, F5, 82) (dual of [228, 120, 83]-code), but
- OA(5121, 148, S5, 93), 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.