Information on Result #1875683
There is no digital (77, m, 643)-net over F9 with m > ∞, because logical equivalence would yield (77, 643)-sequence in base 9, but
- net from sequence [i] would yield (77, m, 644)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (77, 1928, 644)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91928, 644, S9, 3, 1851), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 846440 839975 228413 672308 093506 402136 149881 189064 356118 344251 312448 741409 897297 319674 421706 686078 912395 606371 369434 786611 549579 752095 497648 921633 804032 205975 891294 251303 989413 458824 016227 189485 788455 303248 642447 905374 619459 790216 255976 130482 300358 625018 466072 560336 165599 022789 344162 239457 596629 680900 098547 456492 313731 390031 987354 320613 372534 871269 559078 538831 839628 310976 994324 789058 378853 637191 413049 885410 671658 485794 535013 929502 582895 055636 467728 262604 720896 670238 868884 902045 995437 069162 718668 626029 077652 052871 469967 870499 827163 996363 558601 887848 154630 320512 354755 856634 485189 241180 222808 805902 551500 311635 181657 033510 982088 946616 114429 609549 867755 624889 989737 113523 274395 385084 675565 191511 091899 200849 078031 292583 631072 911098 729135 749127 277023 260523 193191 117888 299336 814280 862921 257292 673877 079115 704589 790616 880636 361703 740175 248981 992828 708202 104001 492344 834667 713905 207353 870940 776098 717716 835391 321238 003695 948492 777889 845933 677722 550173 916608 664410 991167 898005 013419 066570 168722 854689 693744 471167 454038 674032 038294 968104 450796 533715 588221 390459 503739 596885 510566 311886 075088 093957 506897 257540 248482 955538 068387 850118 978371 368883 151479 243632 960733 426822 502075 871016 567311 895679 688810 061692 515914 103641 440777 892332 615934 693964 703143 603732 888136 940230 184560 632269 906956 045531 092093 111249 577910 463643 466401 625124 438103 026362 173482 558062 290043 279182 496488 274980 154726 041564 013688 187253 350001 167795 315894 433416 895216 493658 629183 540571 753997 420237 450036 517214 340480 355362 237108 921966 405039 866114 749657 596315 801306 916900 396251 466265 540396 150589 296435 034597 092812 835144 637475 525082 667395 477518 138711 136921 383275 025241 870284 811942 167657 562828 596063 480869 850509 661745 779221 815760 170106 191806 977439 044910 563213 749407 318264 009683 532970 555077 753412 840322 029810 629164 871999 854273 319283 135158 129895 145622 465066 408825 750624 894145 772955 926701 145919 / 463 > 91928 [i]
- extracting embedded OOA [i] would yield OOA(91928, 644, S9, 3, 1851), but
- m-reduction [i] would yield (77, 1928, 644)-net in base 9, but
Mode: Bound (linear).
Optimality
Show details for fixed t and s.
Other Results with Identical Parameters
None.
Depending Results
None.