Information on Result #599757
There is no digital (31, 140, 239)-net over F5, because extracting embedded orthogonal array 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
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.