Information on Result #599414
There is no digital (38, 137, 238)-net over F4, because extracting embedded orthogonal array would yield linear OA(4137, 238, F4, 99) (dual of [238, 101, 100]-code), but
- construction Y1 [i] would yield
- linear OA(4136, 167, F4, 99) (dual of [167, 31, 100]-code), but
- construction Y1 [i] would yield
- OA(4135, 149, S4, 99), but
- the linear programming bound shows that M ≥ 2 040610 487096 181427 758937 498317 933435 839690 422249 792187 355243 784188 300883 648114 289820 041216 / 970 822125 > 4135 [i]
- OA(431, 167, S4, 18), but
- the linear programming bound shows that M ≥ 10 709160 698850 412098 268143 898591 232000 / 2 251884 149854 892341 > 431 [i]
- OA(4135, 149, S4, 99), but
- construction Y1 [i] would yield
- OA(4101, 238, S4, 71), but
- discarding factors would yield OA(4101, 146, S4, 71), but
- the linear programming bound shows that M ≥ 780 391601 299222 805405 564977 076901 757366 079162 890923 638174 195116 932617 997552 007423 809669 824512 / 113 932691 512033 126701 906109 976895 > 4101 [i]
- discarding factors would yield OA(4101, 146, S4, 71), but
- linear OA(4136, 167, F4, 99) (dual of [167, 31, 100]-code), 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.