Information on Result #2026432
There is no OA(2106, 111, S2, 56), because adding a parity check bit would yield OA(2107, 112, S2, 57), but
- the (dual) Plotkin bound shows that M ≥ 5192 296858 534827 628530 496329 220096 / 29 > 2107 [i]
Mode: Bound.
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No OA(2108, 113, S2, 58) | [i] | Truncation | |
| 2 | No OA(2109, 114, S2, 59) | [i] | ||
| 3 | No OOA(2107, 111, S2, 2, 57) | [i] | m-Reduction for OOAs | |
| 4 | No OOA(2108, 111, S2, 2, 58) | [i] | ||
| 5 | No OOA(2109, 111, S2, 2, 59) | [i] | ||
| 6 | No OOA(2110, 111, S2, 2, 60) | [i] | ||
| 7 | No OOA(2111, 111, S2, 2, 61) | [i] | ||
| 8 | No OOA(2112, 111, S2, 2, 62) | [i] | ||
| 9 | No OOA(2113, 111, S2, 2, 63) | [i] | ||
| 10 | No OOA(2114, 111, S2, 2, 64) | [i] | ||
| 11 | No OOA(2115, 111, S2, 2, 65) | [i] | ||
| 12 | No OOA(2116, 111, S2, 2, 66) | [i] | ||
| 13 | No OOA(2117, 111, S2, 2, 67) | [i] | ||
| 14 | No OOA(2118, 111, S2, 2, 68) | [i] | ||
| 15 | No OOA(2119, 111, S2, 2, 69) | [i] | ||
| 16 | No OOA(2120, 111, S2, 2, 70) | [i] | ||
| 17 | No OOA(2121, 111, S2, 2, 71) | [i] | ||
| 18 | No OOA(2122, 111, S2, 2, 72) | [i] | ||
| 19 | No OOA(2123, 111, S2, 2, 73) | [i] | ||
| 20 | No OOA(2124, 111, S2, 2, 74) | [i] | ||
| 21 | No OOA(2125, 111, S2, 2, 75) | [i] | ||
| 22 | No OOA(2126, 111, S2, 2, 76) | [i] | ||
| 23 | No OOA(2127, 111, S2, 2, 77) | [i] | ||
| 24 | No OOA(2128, 111, S2, 2, 78) | [i] | ||
| 25 | No OOA(2129, 111, S2, 2, 79) | [i] | ||
| 26 | No OOA(2130, 111, S2, 2, 80) | [i] | ||
| 27 | No OOA(2131, 111, S2, 2, 81) | [i] | ||
| 28 | No OOA(2132, 111, S2, 2, 82) | [i] | ||
| 29 | No OOA(2133, 111, S2, 2, 83) | [i] | ||
| 30 | No OOA(2134, 111, S2, 2, 84) | [i] | ||
| 31 | No OOA(2135, 111, S2, 2, 85) | [i] | ||
| 32 | No OOA(2136, 111, S2, 2, 86) | [i] | ||
| 33 | No OOA(2137, 111, S2, 2, 87) | [i] | ||
| 34 | No OOA(2138, 111, S2, 2, 88) | [i] | ||
| 35 | No OOA(2139, 111, S2, 2, 89) | [i] | ||
| 36 | No OOA(2140, 111, S2, 2, 90) | [i] | ||
| 37 | No OOA(2141, 111, S2, 2, 91) | [i] | ||
| 38 | No OOA(2142, 111, S2, 2, 92) | [i] | ||
| 39 | No OOA(2143, 111, S2, 2, 93) | [i] | ||
| 40 | No OOA(2144, 111, S2, 2, 94) | [i] | ||
| 41 | No OOA(2106, 111, S2, 2, 56) | [i] | Depth Reduction | |
| 42 | No OOA(2106, 111, S2, 3, 56) | [i] | ||
| 43 | No OOA(2106, 111, S2, 4, 56) | [i] | ||
| 44 | No OOA(2106, 111, S2, 5, 56) | [i] | ||
| 45 | No OOA(2106, 111, S2, 6, 56) | [i] | ||
| 46 | No OOA(2106, 111, S2, 7, 56) | [i] | ||
| 47 | No OOA(2106, 111, S2, 8, 56) | [i] | ||
| 48 | No (50, 106, 111)-net in base 2 | [i] | Extracting Embedded Orthogonal Array | |