Information on Result #1881316
There is no digital (58, 58+k, 1567)-net over F27 for arbitrarily large k, because logical equivalence would yield (58, m, 1567)-net in base 27 for arbitrarily large m, but
- m-reduction [i] would yield (58, 3131, 1567)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(273131, 1567, S27, 2, 3073), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 730 833184 129179 875185 657348 344892 521502 548600 946873 749777 216291 083567 229640 549025 119563 391414 600658 622143 059042 204883 829705 822757 980437 133310 196048 028676 138510 109265 345582 011851 694432 455921 716543 970381 795914 024473 649734 397919 127070 953790 102976 074454 011196 478027 968737 756568 704156 932404 349978 788487 684499 771807 490575 568555 376447 799672 578309 158818 531449 482497 495350 797275 571766 243744 179808 848827 808467 771939 893405 276458 136583 483588 575217 122548 847277 430358 287155 304440 750488 815228 468483 846177 648440 443906 791793 311316 426007 279616 501560 575000 692872 360492 848471 737336 768330 336364 116938 576128 015340 138246 623076 421525 628036 591703 380001 124073 802277 563903 553669 564311 905774 976151 958576 172173 900421 270271 735902 109528 464954 454396 553460 651889 905669 209820 459134 873924 159958 953507 613083 730385 839108 950889 925189 223959 839217 435852 496017 153507 102218 516602 010191 793566 730003 196476 798504 649041 900690 035820 396300 503272 884706 098895 987156 973139 040199 731281 599822 561407 706015 106447 987912 103473 556541 491552 950215 977006 163885 795978 227000 346575 015965 399490 046424 353396 293505 184430 674513 602473 874176 212224 263997 179285 183567 773927 689529 004953 775234 279494 814702 132790 149728 885124 399190 613641 663216 698305 948838 661783 611441 053283 336487 330433 940693 621155 854987 167134 120319 689389 758446 773057 872549 142188 712241 104696 580909 911935 404738 631023 499915 570913 964615 397959 611789 950974 897088 823032 124278 880317 200273 705795 992837 854596 829352 224634 929391 055391 255748 735758 985949 044276 601958 188505 016765 971144 046145 698737 653134 795581 338455 997332 607807 390099 903772 225625 994632 191941 893968 099560 154702 581630 620402 650791 961812 862583 650240 157232 840320 891512 862462 545859 464626 319227 365041 564256 872735 363633 008588 059628 380571 465620 374107 534851 388713 222896 158627 353262 332693 195451 099428 181687 188429 543304 650572 934440 311995 612816 260108 540125 750223 685940 683360 350955 624871 391940 636149 991082 233702 001682 978027 589193 011720 163204 472453 222131 511052 742542 683952 815971 449778 589402 519149 349967 487990 154225 508817 453008 220443 973734 385676 755148 205649 924304 484606 568947 758153 042611 869891 350265 232671 657365 625873 666990 796402 948531 382633 729179 912566 430838 639585 138691 220597 296369 160761 208632 341609 582753 103830 803636 624593 995926 044589 584084 154510 858214 243231 451777 808282 010471 051246 419900 145132 816163 169754 930651 083857 548731 131514 324327 269849 749121 236700 445628 668199 037595 842475 682309 714984 048003 866891 735677 111259 928903 920510 612675 092824 490851 108776 491740 342973 711951 546562 532764 910537 775518 597118 782355 000569 146302 664322 359104 732963 169302 895858 498734 556401 867715 730634 489620 506330 066652 746786 278284 734071 496245 044983 208752 676651 321662 570044 610900 565508 798320 265941 368770 627526 216656 565225 615654 047922 610662 681534 256839 356796 332946 894037 240951 493630 046451 999694 279186 958242 297020 746008 816407 720738 765685 957351 996663 815488 185343 166728 312795 826524 380837 206963 749637 914038 404548 008053 325986 640355 395880 406243 101678 757591 509872 484002 246828 182612 435201 341809 832929 528088 615494 441442 437837 063826 541417 260198 171606 772979 406213 729526 564389 437382 945300 002971 264866 351142 270005 633893 975786 681871 606551 408352 501217 376435 056022 148221 784064 502275 737547 396123 979492 134944 038332 369612 402662 260560 652752 994081 395907 083006 375322 121859 023752 348564 576363 527316 065937 911366 809148 097532 345735 949811 153561 749648 715718 875229 404947 115925 660870 864888 880216 923069 047829 955560 674090 491123 985648 407253 052996 897759 087139 632248 610831 481787 793443 814412 317129 196408 315879 590186 921159 358351 306155 848977 223667 755756 989239 789838 488689 163606 535528 024225 611407 128304 549533 130583 618734 311762 946722 434563 341412 726814 451040 145225 918012 686195 442942 337094 860388 370009 017943 761570 372007 796693 887549 368733 501186 418118 302442 089850 202841 131562 360026 517738 130744 356585 033846 478075 944863 080353 867392 016385 902334 369424 448437 927201 222890 945719 173145 352209 069064 583968 437263 835670 433702 685936 513944 407030 448263 322255 724892 157181 853085 150981 655113 378632 412779 868440 561682 425039 578463 042013 141274 625482 819261 862563 154733 975322 876511 285246 384992 809397 130563 217691 064017 211746 938349 428760 122620 238991 256715 476150 926045 475318 591467 752953 788346 146803 175771 554343 100806 603216 293533 328628 484816 604648 152193 792964 578033 182618 231944 896267 016973 313016 162593 003919 017061 488350 787142 599261 532510 793489 108573 685286 078812 397328 411094 403175 770501 697436 471326 365236 547615 176704 861948 083500 651749 395456 443090 031288 223143 280302 810378 195986 026952 390936 429798 430794 740912 213510 846461 998827 897249 026316 101350 211599 620306 997210 033852 208281 349494 055663 693882 108879 220688 826407 277513 954759 964547 545597 453449 241154 631898 839328 797828 / 1537 > 273131 [i]
- extracting embedded OOA [i] would yield OOA(273131, 1567, S27, 2, 3073), 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.