Information on Result #1880442
There is no digital (74, 74+k, 620)-net over F9 for arbitrarily large k, because logical equivalence would yield (74, m, 620)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (74, 1856, 620)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91856, 620, S9, 3, 1782), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 30635 285044 634559 125906 124534 627929 767990 414695 771112 299481 412838 694727 041365 645799 530409 142556 447165 294524 509939 876900 012089 113022 773344 409798 373404 970511 129225 972285 013933 642912 872453 099917 939728 221247 818681 252922 356694 496761 008624 439418 069213 930615 254983 368611 003723 740587 917912 361840 855728 119809 890496 207212 749922 004962 526539 026126 232560 640346 400847 720214 400923 873998 362152 106474 532758 184564 467580 260606 510212 259139 197652 015137 952783 077156 564199 745317 335593 957933 528045 918731 802607 098291 447505 425110 879314 427811 749879 198407 269768 653994 994664 581131 866041 992306 581561 706154 352914 699586 909125 212421 521379 105752 233259 299717 164458 453204 088766 209783 518025 781008 042202 227921 517952 098564 876709 084801 564507 644086 502972 171122 590787 587073 515628 809722 628843 272754 013177 760424 399411 606690 922358 991818 679417 496849 907405 304629 344107 884022 617469 752755 482466 637621 202459 141611 973847 162210 184439 067107 059049 117183 979332 095742 044758 858336 880430 388522 695882 165328 978627 889513 856220 666671 530976 768422 782576 899976 510675 278065 032039 756321 303724 842813 106211 690557 978357 918982 032066 192754 173109 014573 141863 265650 170054 307761 962194 394735 669193 578285 086822 702723 747077 118615 500285 368017 885064 590554 939332 814354 649595 450135 790262 989773 666614 007947 642026 435937 253938 745005 094655 355532 980222 764490 372627 672766 407269 145539 880525 753755 512350 266433 805381 295364 910592 293171 449484 833962 900030 314702 052768 524093 784356 139200 241097 009436 659522 021272 882287 918150 006865 567918 279193 950314 012355 388716 541798 189804 223437 050732 218860 606123 123435 253125 162205 048540 994655 560390 338904 858438 264944 062154 624721 238402 367193 599377 389956 114592 932166 353686 046044 667293 117018 509705 272835 444501 867245 920770 162773 439550 681483 311300 711883 554503 407193 755788 893556 499835 356305 222459 477057 774890 212331 126757 991859 712316 150139 054103 / 1783 > 91856 [i]
- extracting embedded OOA [i] would yield OOA(91856, 620, S9, 3, 1782), 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.