Information on Result #547962

There is no linear OA(5130, 192, F5, 100) (dual of [192, 62, 101]-code), because construction Y1 would yield
  1. OA(5129, 148, S5, 100), but
    • the linear programming bound shows that M ≥ 437019 493054 884386 993159 269280 163944 474914 010322 994172 449412 913421 078197 284685 984413 954429 328441 619873 046875 / 236583 689197 696731 > 5129 [i]
  2. OA(562, 192, S5, 44), but
    • discarding factors would yield OA(562, 190, S5, 44), but
      • the linear programming bound shows that M ≥ 5 531619 630605 621733 791634 558919 444104 118885 526484 067787 791939 510637 894272 804260 253906 250000 000000 000000 / 236416 842360 352611 941840 260955 732881 660879 805306 461094 587839 > 562 [i]

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:

ResultThis
result
only		Method
1No linear OA(5131, 193, F5, 101) (dual of [193, 62, 102]-code) [i]Truncation
2No linear OOA(5131, 192, F5, 2, 101) (dual of [(192, 2), 253, 102]-NRT-code) [i]m-Reduction for OOAs
3No linear OOA(5130, 192, F5, 2, 100) (dual of [(192, 2), 254, 101]-NRT-code) [i]Depth Reduction
4No linear OOA(5130, 192, F5, 3, 100) (dual of [(192, 3), 446, 101]-NRT-code) [i]
5No digital (30, 130, 192)-net over F5 [i]Extracting Embedded Orthogonal Array