Information on Result #1855968
There is no (1, m, 515)-net in base 256 for arbitrarily large m, because m-reduction would yield (1, 513, 515)-net in base 256, but
- extracting embedded OOA [i] would yield OA(256513, 515, S256, 512), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 68 445069 732292 362678 550705 649524 695536 760537 025569 343431 261125 560497 203312 823989 492044 713946 971999 983428 574033 637491 529350 353612 844944 169845 603440 253427 074855 466236 414768 578451 233937 171046 971363 454357 996296 991291 891798 431458 768502 500382 125873 206828 564270 803104 943551 550015 671418 232413 166925 773392 025880 428982 235232 788924 844339 816407 380148 941003 134039 060173 518884 243157 578092 316263 446767 197730 518829 740447 207252 642462 847352 039960 379177 965178 838885 302040 992165 989013 848615 620553 938938 647927 229712 496858 776833 279261 646282 385780 442085 051388 778065 958786 410528 848040 328747 179581 476059 611024 615823 427820 755070 123520 466421 272183 171530 464351 075161 563469 421518 658131 346731 676349 386795 844742 545845 465611 310197 744364 379851 022344 177845 200955 581101 505432 159086 156942 658389 351257 285203 760530 907744 160419 338635 375694 547158 110386 472161 207576 558809 448587 130529 099794 538754 765004 210661 814807 751545 523442 263154 829218 042438 001036 224293 511949 628757 957439 699710 633572 558555 150140 274981 198251 114696 533593 030399 806634 013607 501812 053996 330513 574084 619686 973962 526355 171937 537724 790986 936925 970320 384649 646540 083524 862111 968566 765871 048188 564498 804231 669218 139002 567239 146086 471165 739093 354968 985745 927255 915987 673520 729016 351983 759267 610217 985365 796661 113017 860096 / 171 > 256513 [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 (1, 514)-sequence in base 256 | [i] | Net from Sequence | |
| 2 | No (1, 1+k, 515)-net in base 256 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (1, m, 515)-net in base 256 with unbounded m | [i] | ||
| 4 | No digital (1, 1+k, 515)-net over F256 for arbitrarily large k | [i] | ||
| 5 | No digital (1, m, 515)-net over F256 with unbounded m | [i] | ||