Information on Result #1851054
There is no (87, m, 278)-net in base 4 for arbitrarily large m, because m-reduction would yield (87, 1106, 278)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(41106, 278, S4, 4, 1019), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 78 592978 525324 669157 800681 863520 102695 144898 106700 624187 068521 735050 911221 411947 896448 185883 205880 881052 592529 037124 592454 272790 134306 281445 736545 277106 192492 382190 036887 928994 738787 212731 076367 856640 636226 184499 178641 375424 089328 974978 350473 793417 224229 045608 745874 935864 827124 510338 008437 876854 457241 912124 581236 024602 659922 738265 880257 324160 963680 033087 913321 399945 819640 929176 726896 539423 655243 788532 843906 893127 219815 575337 347668 966227 142966 198588 586117 492790 245508 339671 518475 344744 088190 458438 517447 181666 508888 667810 635687 978213 140599 303179 811381 483026 635551 790877 544387 549239 204922 520423 101282 386675 322035 936687 345181 393003 681907 727795 222337 412821 282910 633984 / 85 > 41106 [i]
Mode: Bound.
Optimality
Show details for fixed m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No (87, 277)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (87, 87+k, 278)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (87, m, 278)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (87, 87+k, 278)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (87, m, 278)-net over F4 with unbounded m | [i] | ||