Information on Result #1878746
There is no digital (214, 214+k, 443)-net over F3 for arbitrarily large k, because logical equivalence would yield (214, m, 443)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (214, 2651, 443)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32651, 443, S3, 6, 2437), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 92 268615 879519 380795 564627 034845 061534 562423 217225 962520 221625 313639 121643 718066 938722 695230 448090 711554 463650 002847 746196 906269 673141 598960 903612 387429 092163 392352 126303 313143 105991 898018 095876 007877 622794 538476 853396 834028 248376 106355 529901 600404 224647 954551 133289 203021 208322 953194 084250 299471 668097 751364 336021 542016 225349 662740 098801 696784 578120 880775 966127 917330 733508 946942 980262 581298 760662 957144 874986 007898 630223 148045 350305 000826 681112 456797 385107 916913 679849 509586 600136 294487 965732 285342 990964 901924 079316 861666 960880 723940 415588 584872 008549 106559 559433 896862 114895 525461 557093 620828 612427 149572 271616 049312 762370 614138 245056 952788 401694 454476 146255 545074 657180 038794 495733 675911 128670 578199 280300 051650 781681 710882 062735 599733 192207 966012 507786 713683 142862 601586 006442 363101 143425 579666 735399 786937 006181 481237 634172 273814 774335 374887 414634 377177 774901 065846 203986 169593 569982 657409 275757 721500 728081 962457 847769 547694 340948 153870 378835 821563 899235 082692 203107 972118 582845 407499 835057 767950 351384 462066 285118 106230 730327 371628 455414 703102 299353 902076 850679 586658 118215 089309 348694 781628 968767 882258 057499 739098 106040 233558 321279 775246 090008 544948 564883 696527 897678 226964 456999 972771 267325 899250 349798 330542 924471 698647 462141 399630 814750 726276 402001 929076 / 1219 > 32651 [i]
- extracting embedded OOA [i] would yield OOA(32651, 443, S3, 6, 2437), 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.