Best Known (37, s)-Sequences in Base 81
(37, 729)-Sequence over F81 — Constructive and digital
Digital (37, 729)-sequence over F81, using
- t-expansion [i] based on digital (36, 729)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- the Hermitian function field over F81 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
(37, 3115)-Sequence in Base 81 — Upper bound on s
There is no (37, 3116)-sequence in base 81, because
- net from sequence [i] would yield (37, m, 3117)-net in base 81 for arbitrarily large m, but
- m-reduction [i] would yield (37, 3115, 3117)-net in base 81, but
- extracting embedded OOA [i] would yield OA(813115, 3117, S81, 3078), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 269 391217 400609 499238 784164 434848 358817 827194 680041 086234 660980 568965 611424 623551 411079 982228 889309 612048 281540 820113 177029 729005 346805 328145 663786 057130 818747 122549 669050 675336 948070 550490 482297 212122 448501 056778 983086 585025 525647 861988 147350 092758 162644 721935 012294 349101 554896 327668 921850 321928 092809 193735 278938 334580 497254 318722 143522 977601 533800 414321 878609 831960 124911 224740 292549 205220 060484 271866 263847 728200 320260 421452 665957 920576 446985 692122 136376 675068 538183 003894 795687 016156 552335 132415 546371 674875 325572 773559 820312 869380 553400 677826 607122 576691 379406 446571 238255 164500 258267 128072 627799 584839 866951 059738 748857 838329 809524 844517 034958 993046 658255 941321 274595 470349 747443 181985 548580 029403 297452 770958 710962 315221 651951 783482 117397 243928 262502 829311 133824 813977 665239 219486 183096 537863 387964 686052 229532 063716 841679 377368 170585 071131 110583 357290 678445 499134 328520 819711 698415 669473 923024 715427 301025 725892 182001 644319 384998 443228 962222 117328 608296 387486 817751 204832 493069 723999 845659 721769 239953 120749 046276 904190 511622 304616 075534 174261 665339 761843 729400 422298 632915 600843 025991 406727 978121 437569 761171 560690 937721 547730 856157 884067 694223 093418 043691 858874 852934 261733 019358 521942 288618 400652 607604 134674 018733 431830 226652 378301 282451 930261 672957 656547 683943 738138 798153 134202 964885 648925 014833 031899 698274 272707 813133 098614 046628 948372 479579 827063 231221 229065 251689 332448 086104 695307 968196 629321 680084 316475 611627 995574 481229 758223 011157 675902 316269 619609 671582 030004 644207 335520 090645 807256 915457 388700 666276 706020 518740 430511 572587 758410 068566 425465 208295 941441 130336 216234 206827 390878 767010 658633 125718 896940 226272 987705 390407 873394 823521 449186 174017 516608 315594 971953 439936 815972 327342 546919 762032 894800 076939 440341 844536 248039 910708 095281 648594 389412 090638 247393 485812 542239 195369 011843 567894 251999 921781 866890 742099 409520 259568 128313 799157 674684 657314 869376 667741 044854 737002 946055 672234 957690 581127 272269 096989 346835 049802 299334 045569 014331 966594 548091 568195 669708 001196 720938 103954 890171 118958 459214 926067 165848 850287 001207 001824 717693 445517 975112 063686 159096 515857 462834 910621 960345 695319 907608 039243 610187 307326 077634 796793 190723 632590 948458 516025 870911 924083 069796 955721 129930 739957 568202 103966 565639 211688 917768 776863 052100 406293 976799 411253 849089 354440 887712 558599 874668 050499 587271 667110 809102 212940 446621 628378 385124 745817 302574 387438 747566 845572 119192 312501 489415 804839 395885 675238 481073 463204 965167 887214 051472 221371 122143 866354 331377 897122 842150 898554 779551 403671 938181 327656 487460 867191 358159 262287 861923 839244 064106 853334 163475 522950 177936 345237 832605 069127 688442 250906 081788 095891 384910 586379 252740 055989 229063 511618 201228 399249 207348 524491 564463 308826 296809 825599 488942 077193 380217 950688 358399 074491 798617 009154 258510 439622 030076 346198 393796 134561 789983 916637 970762 437503 637128 297674 315065 096144 923162 743058 555372 250703 601605 402867 444806 625868 040641 365605 753656 012191 962140 063779 636524 010163 303234 508752 981994 548006 245508 987123 820937 952478 549004 365729 245580 231294 776017 907084 051922 438528 917604 728987 807479 177436 961684 316393 494834 435826 627218 781602 690248 645267 116418 107575 816107 222956 415873 930261 031328 548782 018356 589246 378433 288117 692599 218542 143944 239649 624137 455761 894340 231643 659753 782136 010621 228582 485874 072890 241822 824168 939836 715780 614755 099959 052142 202856 996609 353787 266472 994064 970344 878410 122168 490991 012935 522206 404309 952530 013247 736776 225543 292055 439851 373018 770567 524391 107277 455391 553266 921633 665625 464319 360110 971290 481000 599067 080310 745413 799367 490036 619391 846583 518915 070308 700204 251036 770676 272080 101636 873657 611031 426761 252877 219128 858994 054114 104836 510837 121979 144229 152734 253367 133475 472550 983604 754710 793868 370535 402398 945540 919393 262060 284300 380004 168621 330367 358064 582941 175384 897443 636823 022298 832320 923745 967967 209994 277988 248906 056366 822348 377061 818771 282374 184119 007382 611562 332394 401849 174236 357217 981649 492318 924154 936738 003785 487258 556147 622385 148871 984333 782327 494630 156466 057829 443714 562065 368690 903525 837690 454737 749046 449257 647620 988121 914383 231620 726530 816673 002804 580197 302504 972071 278450 224476 113095 639755 270617 604812 979351 875800 092863 487830 622708 579231 621754 622835 654995 083554 513939 117610 995976 529895 286453 724465 051902 088065 795352 437250 689495 831364 919796 804999 442635 534433 138025 402223 539147 827535 845274 323279 870431 701052 410342 767021 442758 029943 554728 211528 087851 644039 404857 736592 203282 037150 657581 020498 679757 019195 664545 915621 804727 779069 050245 224120 179223 999553 374455 681849 292728 029785 671211 285914 130142 147462 654916 327669 684218 448592 333612 006949 377752 115016 788632 136145 881568 364485 015958 106965 245960 427994 790453 277285 546707 043778 454243 587649 626208 172113 486949 719683 106590 958234 839261 898310 808961 215607 048304 741924 921806 415663 447051 131775 895768 421387 569109 177094 782128 323947 371925 422392 734503 751919 585264 024191 887317 591352 372348 782420 411669 624100 640119 581872 610907 419189 041255 026353 901389 942380 887845 755311 448805 320609 681378 445424 485500 459666 527134 250966 420177 786221 724829 367507 741547 827334 121244 142795 233756 095370 473211 639351 111155 929661 585913 316333 663333 321797 054278 606689 344905 548329 615711 367806 750447 980749 495869 824199 656054 672797 354877 789029 015049 371244 213163 821745 065950 496404 101577 452636 014977 892683 461654 381520 924470 734815 421413 168283 648572 117951 618764 759066 499883 093897 247931 258545 775535 713289 089088 899271 333469 009398 559078 732274 392024 490750 649470 186298 213024 563577 922398 106059 927919 671747 242985 393020 031068 919687 173986 916630 147015 729020 605910 492899 444457 641572 190810 352308 651199 625731 015954 723765 893850 891111 297249 005103 817027 047917 275156 695149 443084 729858 532259 444099 673562 895502 306417 853352 481738 598420 476848 086220 760716 141772 292042 877234 825908 189036 288020 918191 873398 452443 481934 638844 514732 215195 627382 325440 065586 967352 735602 183992 207867 482015 615058 887788 256129 832322 183530 180941 846673 834480 803398 065844 994555 195491 711373 594855 421347 564659 641100 601754 993448 180862 449812 004327 931650 543095 239980 669498 874834 225803 981074 878694 827807 670649 132597 354024 633959 / 3079 > 813115 [i]
- extracting embedded OOA [i] would yield OA(813115, 3117, S81, 3078), but
- m-reduction [i] would yield (37, 3115, 3117)-net in base 81, but