Information on Result #1852632
There is no (87, m, 635)-net in base 8 for arbitrarily large m, because m-reduction would yield (87, 1901, 635)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(81901, 635, S8, 3, 1814), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 237 752593 456322 407493 363322 360564 814560 464017 531194 932742 223184 495655 000003 294181 239647 061164 747846 610971 421278 339460 650179 995689 115782 583804 320823 103413 308564 680821 630546 566976 905576 249518 363076 114609 607433 524321 976767 158900 255260 320201 732011 781935 125814 651432 616046 194004 797482 834118 241457 687234 340216 342159 889375 524687 868159 477541 123343 761959 191014 461962 812256 757758 198589 695717 709298 402171 216840 177583 221485 224919 732229 316689 453141 483022 586257 129457 315570 793850 637624 402913 067652 247931 312982 352264 946423 389529 315636 674824 974521 543050 065439 991291 451648 075398 080601 730237 644034 545149 240071 873924 782702 670330 234246 412848 245213 845291 291515 029762 328889 124185 246066 961089 207989 098463 028009 148231 337531 813406 126657 304875 004844 188553 224141 377560 243548 003432 098899 152088 773785 658184 183087 502230 020197 853501 037827 751013 137573 173118 441921 499521 363024 909941 766018 535943 363170 811945 126515 741559 841912 675505 789729 745609 330508 930811 011727 687988 927750 094774 664854 459276 036883 245295 963600 000704 870730 105973 972920 624252 893809 043828 208801 904376 813713 858173 979126 702449 335323 161026 735366 349881 803593 006672 454658 600787 293624 920495 655979 986207 345057 648107 198890 687734 088032 654575 888238 777709 689752 977950 542130 377081 120602 077224 445745 473702 089888 451521 387081 044654 586751 862426 125083 951440 373007 733487 084736 364404 759671 374244 113848 221397 438916 909098 672618 042358 096337 056457 834146 505342 906618 137724 386437 976002 733087 036619 623788 302766 698130 841747 143577 845540 591626 775484 217347 006161 097544 509466 985466 415714 783280 673176 022574 425173 610758 081452 283611 501016 561950 381687 917342 055760 736341 896721 489550 178949 647663 284954 087701 244645 801624 789939 332364 912073 617787 155872 697275 648580 605733 302063 725103 203338 246408 071020 917003 740554 555684 076986 040320 / 33 > 81901 [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, 634)-sequence in base 8 | [i] | Net from Sequence | |
| 2 | No (87, 87+k, 635)-net in base 8 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (87, m, 635)-net in base 8 with unbounded m | [i] | ||
| 4 | No digital (87, 87+k, 635)-net over F8 for arbitrarily large k | [i] | ||
| 5 | No digital (87, m, 635)-net over F8 with unbounded m | [i] | ||