Information on Result #1879830
There is no digital (93, 93+k, 582)-net over F7 for arbitrarily large k, because logical equivalence would yield (93, m, 582)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (93, 1742, 582)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(71742, 582, S7, 3, 1649), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 41559 240442 046092 600024 046679 232475 196866 975323 282854 964050 725499 455708 415355 246896 798614 386613 331109 208059 341909 049175 561599 307590 219388 649413 343448 736205 764546 067643 946378 336548 504644 092620 907555 096941 733692 781227 831032 317485 245940 749621 138525 355835 643374 467555 594803 921877 380714 776516 988102 468567 859314 700201 103141 970869 793494 084357 651279 963633 181435 530828 258665 230546 560565 392427 458980 408950 737869 274780 474156 884181 879716 792268 951049 736989 864425 036006 797429 822436 099049 526960 200522 960728 113204 913537 285617 557359 942948 397251 357998 084381 864850 524117 168422 117303 585513 450664 349847 034707 132832 796776 595031 439516 634596 456161 806314 513828 576567 618559 517487 500252 414682 742640 854452 597369 971717 079143 201619 310353 429581 515828 692041 023140 521797 097153 114901 052731 943666 308404 418765 347594 593133 847524 661312 640774 157712 392426 673107 022608 882829 071728 908309 378070 374453 961696 352367 346409 412246 774990 927750 496560 871513 575609 047320 933904 822946 569346 972423 209830 643931 259934 815134 732647 869126 273930 934575 956988 035603 444251 251074 452629 721845 636450 686144 563336 833105 298801 878665 696856 852203 447642 720799 249154 923434 141105 609535 221577 595087 191153 667051 776065 391466 972023 541824 487776 255966 761978 951935 069493 482473 103963 411495 084824 035243 074596 159004 709699 374917 170397 634198 159745 259574 823450 898974 394947 874318 572994 656906 332313 034886 320570 919922 375132 088617 429946 493563 216477 284676 600866 530008 292038 175658 982607 735923 091075 571589 441071 267994 358389 905595 974041 714725 553953 670103 716095 482179 386063 / 275 > 71742 [i]
- extracting embedded OOA [i] would yield OOA(71742, 582, S7, 3, 1649), but
Mode: Bound (linear).
Optimality
Show details for fixed k and s, k and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.