Information on Result #548077
There is no linear OA(5112, 252, F5, 85) (dual of [252, 140, 86]-code), because construction Y1 would yield
- OA(5111, 143, S5, 85), but
- the linear programming bound shows that M ≥ 220 445839 236062 243251 966630 886846 194373 438661 017264 989094 781670 909972 692840 028685 168363 153934 478759 765625 / 378 761134 914432 479453 277033 > 5111 [i]
- linear OA(5140, 252, F5, 109) (dual of [252, 112, 110]-code), but
- discarding factors / shortening the dual code would yield linear OA(5140, 239, F5, 109) (dual of [239, 99, 110]-code), but
- construction Y1 [i] would yield
- linear OA(5139, 164, F5, 109) (dual of [164, 25, 110]-code), but
- construction Y1 [i] would yield
- OA(5138, 148, S5, 109), but
- the linear programming bound shows that M ≥ 86 158555 819318 512642 331328 682663 835348 540649 443889 196923 328992 021307 026760 723601 910285 651683 807373 046875 / 29 425011 > 5138 [i]
- OA(525, 164, S5, 16), but
- discarding factors would yield OA(525, 148, S5, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 313081 833470 800945 > 525 [i]
- discarding factors would yield OA(525, 148, S5, 16), but
- OA(5138, 148, S5, 109), but
- construction Y1 [i] would yield
- OA(599, 239, S5, 75), but
- discarding factors would yield OA(599, 147, S5, 75), but
- the linear programming bound shows that M ≥ 10 465163 072971 841494 226679 044239 098519 996159 375872 949750 717770 995481 826038 130942 490580 153891 865933 246663 189493 119716 644287 109375 / 6623 020670 394833 160024 516013 529216 797975 034523 571498 254336 > 599 [i]
- discarding factors would yield OA(599, 147, S5, 75), but
- linear OA(5139, 164, F5, 109) (dual of [164, 25, 110]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(5140, 239, F5, 109) (dual of [239, 99, 110]-code), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(5112, 252, F5, 2, 85) (dual of [(252, 2), 392, 86]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(5112, 252, F5, 3, 85) (dual of [(252, 3), 644, 86]-NRT-code) | [i] | ||
| 3 | No digital (27, 112, 252)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |