Information on Result #3143179
There is no digital (136, 249, 384)-net over F2, because 1 times m-reduction would yield digital (136, 248, 384)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(2248, 384, F2, 112) (dual of [384, 136, 113]-code), but
- construction Y1 [i] would yield
- linear OA(2247, 332, F2, 112) (dual of [332, 85, 113]-code), but
- construction Y1 [i] would yield
- OA(2246, 302, S2, 112), but
- 2 times truncation [i] would yield OA(2244, 300, S2, 110), but
- the linear programming bound shows that M ≥ 727209 932038 995964 963694 786156 506719 769259 430085 807852 102717 045283 079365 167115 254635 995296 956416 / 21378 491075 472167 578125 > 2244 [i]
- 2 times truncation [i] would yield OA(2244, 300, S2, 110), but
- linear OA(285, 332, F2, 30) (dual of [332, 247, 31]-code), but
- the Johnson bound shows that N ≤ 220 247871 551638 926977 652794 793575 888633 238636 124356 543746 403131 692235 320146 < 2247 [i]
- OA(2246, 302, S2, 112), but
- construction Y1 [i] would yield
- linear OA(2136, 384, F2, 52) (dual of [384, 248, 53]-code), but
- discarding factors / shortening the dual code would yield linear OA(2136, 374, F2, 52) (dual of [374, 238, 53]-code), but
- the improved Johnson bound shows that N ≤ 2 360702 811474 389063 749944 041391 364709 858504 534718 295956 994191 765553 370834 < 2238 [i]
- discarding factors / shortening the dual code would yield linear OA(2136, 374, F2, 52) (dual of [374, 238, 53]-code), but
- linear OA(2247, 332, F2, 112) (dual of [332, 85, 113]-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.