Information on Result #599996
There is no digital (16, 108, 1561)-net over F27, because extracting embedded orthogonal array would yield linear OA(27108, 1561, F27, 92) (dual of [1561, 1453, 93]-code), but
- the Johnson bound shows that N ≤ 5873 828340 592555 486712 533937 129111 298020 640571 151314 031868 448305 042913 062168 320322 398045 840513 371424 266411 919636 164467 953203 169374 206447 375165 734593 669233 001061 396160 773523 512109 448333 626518 125177 583545 249471 535061 923989 913429 492842 134597 683681 187958 794560 903542 983107 908995 286161 387979 976208 103644 161545 515734 234559 362078 291061 335294 360808 300760 046431 363666 853600 170892 964857 482326 103443 560028 253993 232185 763928 554377 665222 473279 472469 266553 172414 776976 217016 099414 945490 061203 250855 245693 545252 365250 824650 465627 697448 392027 328245 684738 327546 173622 581311 435281 698867 592535 829573 652935 391399 963231 166652 840775 506459 086116 395314 192333 637818 543515 261771 255438 350348 468234 875318 804106 767751 781648 725777 579044 077954 935658 180289 712184 761086 337805 138328 269534 555067 980786 669107 813180 782575 442070 437248 771215 825274 916402 687809 882215 616862 639180 599763 031932 921190 345836 416068 274558 064937 482316 703667 740646 885624 596062 252300 720876 961581 641146 954894 676581 377643 906425 854810 611478 480920 184835 286206 226294 918619 472241 816448 761545 628861 807832 144208 414692 764407 464043 399226 315754 377156 612972 343505 461016 162402 437245 720452 404945 570571 208756 351296 892878 200046 815400 941883 533838 733879 143809 880281 583476 507371 211630 742561 185319 018976 636083 073254 545149 098784 095020 464599 151151 477495 712229 095194 772049 070796 567224 066617 610007 452587 320603 578079 169834 287267 772648 173761 940297 898994 004321 248113 171355 439374 233418 186367 802483 107739 989527 236410 461234 919454 325699 558600 739143 358452 023551 402229 209119 396657 030016 799216 147761 386295 304651 329355 962336 916777 245724 819177 781033 247275 338827 094175 221601 456455 823134 135542 187370 753870 176681 185530 094961 796394 019538 147634 123301 686401 694260 277777 103735 470579 493520 582821 771048 455057 084178 545987 162908 260890 739481 972483 852045 374655 232786 979028 041879 314086 956143 146858 560220 207128 968111 111580 491575 462446 519514 659924 560822 175811 210320 949240 202369 470076 740714 158348 404004 627864 132981 867573 623122 723394 847158 969681 017071 125536 478432 041024 285332 356208 544757 090934 253920 749271 118375 840923 150696 026401 813357 746123 173481 335537 435562 198186 350717 267301 078538 801936 134219 937107 < 271453 [i]
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, 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 digital (16, 109, 1561)-net over F27 | [i] | m-Reduction | |