Information on Result #1879230
There is no digital (205, 205+k, 633)-net over F4 for arbitrarily large k, because logical equivalence would yield (205, m, 633)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (205, 3159, 633)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43159, 633, S4, 5, 2954), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 876 076210 166420 226530 060742 047957 422431 805010 110939 410045 125533 176028 359680 635023 576601 127478 376114 079077 214512 745359 536378 903308 754603 444851 607432 030803 302753 806980 923412 310851 863946 550839 047343 600675 028191 609599 976204 252597 739707 499177 721581 026686 631587 314749 033839 306686 150242 251352 103388 221547 404198 797037 383633 904849 942041 241466 554788 640163 034730 812829 544780 409512 006439 164552 947027 725072 195464 014166 156521 659855 088559 540496 696605 480265 533196 986581 069576 885043 176424 619495 834106 485157 349277 997572 438577 648196 837514 176046 128143 940643 086703 271574 394332 786940 411238 366984 456093 569757 383452 931193 226306 940944 641358 775105 417021 724071 550528 063656 203634 390654 310145 908314 784778 408751 505410 941433 369626 149930 599159 286962 915171 878576 292574 991720 243637 025229 203672 108932 242184 672714 899385 472510 095249 852707 256936 124008 020486 060669 599577 480911 193247 729943 346800 054442 168725 656878 695996 466758 580361 632867 208836 079679 374017 652649 315554 266654 691089 203579 360515 269051 312320 846893 058846 153596 320088 120775 295103 363446 567894 307669 771565 727415 542108 735344 156975 951024 659141 933349 356203 013899 541893 109341 241517 815319 613404 507908 965612 462576 912639 710012 176383 024094 898855 961125 161016 020582 010270 573909 219458 557122 595241 278189 665669 738042 040988 533630 045066 652840 165733 103192 793237 493821 578952 000158 483451 398536 975110 780542 594897 065231 641217 224254 713828 965166 571014 630598 267760 831547 305688 309843 683997 049441 827009 903416 812816 066742 159560 987340 935501 877313 689106 964904 609926 129534 155422 049288 038183 164194 084206 232877 771477 822101 826753 058866 300014 124378 568771 086217 347017 335570 957145 773834 485525 335459 305004 312688 332551 487853 550638 447245 215185 102590 357785 338561 874506 401450 845744 885614 493686 493504 535914 538680 157732 419059 709276 460285 203032 305805 866443 277455 412863 901172 584588 567707 737466 982318 753765 557334 188455 201864 284970 158913 820650 999644 709435 632556 169027 617095 808803 823381 279862 456749 914676 481741 764260 283413 062112 772096 / 985 > 43159 [i]
- extracting embedded OOA [i] would yield OOA(43159, 633, S4, 5, 2954), 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.