Information on Result #3142436
There is no digital (90, 167, 253)-net over F2, because 1 times m-reduction would yield digital (90, 166, 253)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(2166, 253, F2, 76) (dual of [253, 87, 77]-code), but
- construction Y1 [i] would yield
- linear OA(2165, 219, F2, 76) (dual of [219, 54, 77]-code), but
- construction Y1 [i] would yield
- linear OA(2164, 199, F2, 76) (dual of [199, 35, 77]-code), but
- adding a parity check bit [i] would yield linear OA(2165, 200, F2, 77) (dual of [200, 35, 78]-code), but
- OA(254, 219, S2, 20), but
- discarding factors would yield OA(254, 195, S2, 20), but
- the Rao or (dual) Hamming bound shows that M ≥ 18304 094847 646336 > 254 [i]
- discarding factors would yield OA(254, 195, S2, 20), but
- linear OA(2164, 199, F2, 76) (dual of [199, 35, 77]-code), but
- construction Y1 [i] would yield
- linear OA(287, 253, F2, 34) (dual of [253, 166, 35]-code), but
- discarding factors / shortening the dual code would yield linear OA(287, 249, F2, 34) (dual of [249, 162, 35]-code), but
- the Johnson bound shows that N ≤ 5 479817 731706 550581 576069 715195 852406 189711 333670 < 2162 [i]
- discarding factors / shortening the dual code would yield linear OA(287, 249, F2, 34) (dual of [249, 162, 35]-code), but
- linear OA(2165, 219, F2, 76) (dual of [219, 54, 77]-code), 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.