Information on Result #3147702
There is no digital (37, 131, 186)-net over F4, because 1 times m-reduction would yield digital (37, 130, 186)-net over F4, but
- extracting embedded orthogonal array [i] would yield linear OA(4130, 186, F4, 93) (dual of [186, 56, 94]-code), but
- construction Y1 [i] would yield
- OA(4129, 150, S4, 93), but
- the linear programming bound shows that M ≥ 334 695053 805711 397561 375492 015414 168229 977994 664798 746384 442171 245301 199155 917928 366979 678208 / 643 455449 300513 > 4129 [i]
- OA(456, 186, S4, 36), but
- discarding factors would yield OA(456, 179, S4, 36), but
- the linear programming bound shows that M ≥ 31 511442 125419 258293 449040 901884 044621 696169 017943 480590 506370 111897 600000 / 5839 126320 766662 475522 447173 784673 305301 > 456 [i]
- discarding factors would yield OA(456, 179, S4, 36), but
- OA(4129, 150, S4, 93), but
- construction Y1 [i] would yield
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.