Best Known (39, 39+∞, s)-Nets in Base 81
(39, 39+∞, 730)-Net over F81 — Constructive and digital
Digital (39, m, 730)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (39, 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
- t-expansion [i] based on digital (36, 729)-sequence over F81, using
(39, 39+∞, 3280)-Net in Base 81 — Upper bound on s
There is no (39, m, 3281)-net in base 81 for arbitrarily large m, because
- m-reduction [i] would yield (39, 3279, 3281)-net in base 81, but
- extracting embedded OOA [i] would yield OA(813279, 3281, S81, 3240), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2777 446989 284709 510564 961725 522798 165397 527154 745346 781202 697478 500075 605650 241673 446945 350517 449784 143132 584592 515650 191522 017778 752060 450859 093990 251445 848295 779107 539098 560493 348183 069955 469012 802664 060028 422072 437257 476976 594876 646699 022725 331401 945969 473148 046367 026532 458989 944111 432482 911082 673425 214823 149349 320285 331021 739803 576369 943393 832778 893579 618904 473797 912215 379128 987481 800106 489780 049219 775500 433877 530816 551012 296244 510132 588154 811679 521740 079490 676434 039974 486538 091280 975077 030794 387406 608657 329612 118433 473892 228510 022034 557405 357640 776748 545099 701463 179976 279976 841546 904353 058476 725505 603094 261399 783304 010835 927287 395309 025770 998224 832562 741261 377520 644280 976014 330297 898528 978037 553297 405492 872426 802115 917242 534877 079356 729746 643321 920513 164878 971997 466759 444771 891445 039583 030294 542011 000468 939936 395034 405675 288363 308937 254130 871837 986761 710946 413325 172248 760116 555765 172042 532627 009931 423989 579727 120509 069765 266438 011053 788778 751887 077225 607316 951283 079808 139535 437461 914628 996135 073089 802517 316627 866629 150142 537128 858627 699942 868550 723908 314454 365442 044535 975388 292731 675779 686294 201180 730542 108125 262857 835057 009897 586879 586806 125518 463766 460912 747157 599236 487195 273516 200920 621673 506373 385156 268452 773316 675653 520262 156690 023520 897526 630406 812079 451166 899094 064429 829530 595315 197777 119254 046378 858699 196260 431231 482598 181171 070955 047386 670041 217140 061810 375384 734566 928644 237197 138232 864684 183391 310503 083797 963754 481232 799118 194408 921022 432814 513925 808153 202008 857521 750841 316690 954017 442434 906521 585010 967553 279852 688974 802601 866151 438279 122498 343426 493877 798946 974111 469317 495742 619560 034599 272578 101688 858170 386319 626060 419921 423343 033734 006860 769442 221345 004673 138623 286210 915757 057722 754230 402230 991906 919862 431968 424185 420161 053145 892580 599831 499741 205704 189746 720161 401788 233766 592525 070902 429113 244583 920544 149003 260106 095134 446299 071762 981469 967889 743493 657677 629430 231219 874947 615763 690724 768398 653944 607918 058095 640825 497960 682112 848129 607771 322736 481943 081263 847068 083838 952814 876276 386645 049791 185767 832141 528304 442451 773843 206989 199443 722346 816772 411278 838653 605880 847466 697282 971655 902667 357288 666490 077996 497106 091225 327711 050192 152847 848342 175207 460478 920363 095693 672389 873683 581157 077044 603556 526075 659338 054494 710538 972169 542569 954735 452745 856185 714427 863794 707792 902007 692132 416002 435939 201635 284185 243476 341546 955382 270132 284779 705922 065217 677439 681509 826632 640019 088921 679042 180071 309549 002933 409447 648754 260264 667374 784215 422520 009771 396897 746334 914764 714539 449149 021412 706873 301292 883694 047988 228003 642525 640310 686075 250644 608683 276326 093554 013893 733657 623875 315579 689326 258818 150473 767457 691441 954536 030793 478228 468662 075635 578153 646577 291075 788731 725003 491592 637796 535995 399847 437458 654345 765169 906433 498983 630658 956213 352134 179242 660481 777751 221757 676638 115990 965477 943512 499220 701716 570067 032219 666262 227182 092555 047660 604969 569980 858404 296630 368337 567014 129877 166428 319600 623920 663924 193332 088634 458120 697712 541358 159906 352605 444715 143614 683323 870036 228617 556892 650359 142236 125316 618724 029955 027906 822560 997401 937513 999603 002231 729638 144310 630096 424114 892336 314143 984954 763122 181485 361820 179873 207005 938371 375280 655720 639215 570926 156997 365754 322152 668371 306512 494894 820492 433980 972819 031142 979886 467035 013170 838666 189326 233657 140594 018628 652485 760462 516247 584141 958693 572653 397660 072442 177191 947087 274488 901759 549637 594895 231984 353771 199686 944700 435732 795023 738520 879358 214280 163232 892956 845698 060856 837782 210544 750541 868815 632526 265539 615740 717260 728245 010479 074339 488455 293780 515018 075995 575949 167234 282642 563221 450357 518388 911682 318097 734888 455273 975496 290938 691810 200179 899833 297032 688057 574957 546091 285274 004381 143388 518384 751318 109320 281031 563033 885600 047961 473828 640394 618414 819594 777996 968252 587896 918671 506624 873034 023023 978268 163528 589028 281624 046381 474548 286087 957785 809095 861810 492642 978031 171286 507540 720413 874072 080938 697216 428719 152490 860841 459025 845101 186374 528272 190349 324032 484759 846092 541068 343356 460043 891573 858239 190385 682524 742601 683153 201347 422074 847106 868665 753197 743764 946444 011579 195102 449169 908307 786323 810142 410707 188756 318287 527915 171186 631623 886495 612182 347868 379178 328325 034824 116096 502825 962307 344105 225910 774843 637543 310148 072612 207293 084262 036393 953985 048879 435040 299397 840754 307860 584779 959714 014179 104489 039923 890466 764085 102294 553964 500814 999154 676080 601344 322269 963362 745687 619342 554621 643358 193219 069026 336911 813679 400046 699391 115647 870819 558644 002019 841264 502430 593507 482382 082692 362428 114958 334906 363710 485681 323175 976647 867383 272021 311823 888934 840686 478961 235637 836971 403368 064341 460551 917386 918824 541636 074674 876379 629626 215603 122366 159046 399093 048945 519140 669376 147801 793868 154693 932942 324565 848172 046098 225458 846336 039372 513402 690514 206152 768291 985540 133419 307948 335396 301030 614319 436789 650234 167965 134490 656452 628979 057673 086825 626449 353690 852401 640292 252817 172469 170102 740034 552215 779769 414166 123808 585370 476963 458227 281800 220646 253905 137325 334186 803014 720403 483358 034004 634854 304425 026777 525301 959235 696351 394282 419032 072180 245511 015904 980061 730541 160759 214344 279809 014722 078171 974493 345478 021386 510059 444623 745001 587453 628334 017581 483720 293504 184951 543296 064230 624207 547944 616188 286493 142806 130245 688922 355398 210126 121869 641946 551963 046439 725979 288572 363148 880293 562316 079367 435282 385683 277694 736767 133732 158191 628369 973864 586739 196243 722388 963610 934720 252732 842725 152563 837479 648219 785734 910301 859531 911017 703400 436602 521694 794909 455904 098629 621233 568119 703256 638058 708212 800701 535784 748228 623750 649378 563883 620585 576516 891100 823925 333524 683866 648886 070146 285130 042328 897044 792291 586038 227108 421731 526635 604069 664651 735337 364280 614726 771444 033878 346139 157537 516550 199353 630236 053607 219218 380015 397415 745880 975761 600826 185303 296724 892351 839622 646942 701054 601445 510833 271120 432284 083084 807843 790714 047425 481700 071514 857917 614843 087065 739335 575067 385299 984760 762766 464300 328847 315680 665791 653720 107049 161046 582330 153545 617451 343420 190103 502755 493755 152316 396126 695445 770619 424561 799781 454595 537309 008695 284993 384209 239947 732989 129868 325890 863550 888970 788438 521388 045964 618882 385505 949711 032000 884917 379924 786805 895613 289168 434148 646765 625704 054930 388008 012652 647507 229266 855929 579965 069171 320794 724576 197821 860950 871261 741113 627297 996883 349391 622441 / 3241 > 813279 [i]
- extracting embedded OOA [i] would yield OA(813279, 3281, S81, 3240), but