Information on Result #599886
There is no digital (15, 113, 256)-net over F9, because extracting embedded orthogonal array would yield linear OA(9113, 256, F9, 98) (dual of [256, 143, 99]-code), but
- construction Y1 [i] would yield
- OA(9112, 130, S9, 98), but
- the linear programming bound shows that M ≥ 102044 798726 074157 946342 526694 215757 184839 498802 434893 273680 913908 810135 229505 295636 373747 351906 016797 225362 681955 238106 940191 / 1 306729 034666 969375 > 9112 [i]
- linear OA(9143, 256, F9, 126) (dual of [256, 113, 127]-code), but
- discarding factors / shortening the dual code would yield linear OA(9143, 217, F9, 126) (dual of [217, 74, 127]-code), but
- residual code [i] would yield OA(917, 90, S9, 14), but
- the linear programming bound shows that M ≥ 536 950364 429691 518020 184925 / 29374 921357 > 917 [i]
- residual code [i] would yield OA(917, 90, S9, 14), but
- discarding factors / shortening the dual code would yield linear OA(9143, 217, F9, 126) (dual of [217, 74, 127]-code), but
- OA(9112, 130, S9, 98), 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.