Best Known (36, 36+∞, s)-Nets in Base 81
(36, 36+∞, 730)-Net over F81 — Constructive and digital
Digital (36, m, 730)-net over F81 for arbitrarily large m, using
- net from sequence [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
(36, 36+∞, 3034)-Net in Base 81 — Upper bound on s
There is no (36, m, 3035)-net in base 81 for arbitrarily large m, because
- m-reduction [i] would yield (36, 3033, 3035)-net in base 81, but
- extracting embedded OOA [i] would yield OA(813033, 3035, S81, 2997), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 41 908380 540215 217375 945943 954281 926009 024950 741519 985846 163059 042982 599794 826903 032526 734757 216041 963610 141891 102053 612741 485225 498680 090423 975082 360774 281998 463598 241392 369092 447135 450421 274069 789880 849149 243833 293509 497073 928560 106979 576922 055626 399317 861737 344256 096014 034366 296902 780634 223325 964137 223244 577664 439834 814902 698736 818228 396973 117883 273750 403867 279980 991658 508220 768596 901715 476278 402137 479106 674707 827975 356916 509404 726934 013591 065989 801983 058540 896107 951681 858040 527495 412605 115997 676217 843345 826785 717424 215327 017516 698308 518747 804287 992022 801124 889082 093942 964993 151886 800815 242997 702104 960494 147571 089968 392938 058667 881363 756086 195536 856715 453327 167424 538184 337109 325982 975458 308441 764184 081587 739423 230231 578367 675930 008413 750720 852516 684632 662968 453136 346990 339028 520724 996233 287479 923866 301530 871755 699797 279264 838922 446780 041299 715088 192147 719644 536849 904863 268224 681827 447943 015531 399373 636808 060993 979949 951051 930927 810130 848085 859813 292041 884224 844458 827284 910158 520540 409094 948585 519604 039280 511306 627185 655369 133026 930976 843849 289992 702943 648997 828662 365710 348039 147387 401789 877648 382277 161752 334804 396447 618589 631298 184639 674022 844736 530964 618241 369201 004693 346978 489609 218330 566526 775282 845667 967548 440540 105277 158456 206693 537505 245989 242387 093993 157460 900527 552953 747035 193048 340212 096177 130591 513282 118815 149724 561511 078018 655916 821223 365579 721123 943020 051720 421006 946153 056198 869625 322950 325175 580373 031357 361477 032098 492892 849003 528600 541580 787295 111161 412910 887846 595764 741372 282926 824159 701131 238467 637684 389016 023786 263030 173441 388511 234705 667391 452080 490956 226877 416851 292674 754730 676411 537973 064391 155939 216402 428561 268120 232698 583564 148015 651282 392406 602972 948034 301301 129359 721095 866645 408670 492567 262673 674467 219437 841676 547208 454294 927238 418002 632944 743028 783860 653563 255971 713517 769300 441980 506302 832422 360082 008076 215674 635609 130609 769676 346331 484561 882649 965867 248900 296159 775760 861624 228453 032971 274003 732386 771195 330294 651534 961970 304221 188234 690980 900052 596355 625327 311071 127499 687196 836727 679280 626195 301276 580861 063588 408236 642394 242422 235852 239752 137540 284073 858296 343323 008625 737245 587083 034250 095660 013929 597567 543686 297757 631767 421448 986668 865230 230296 116388 361255 246952 693953 183822 574027 380182 494982 986030 548495 189933 441776 309239 128255 520878 937937 508777 514746 443415 751303 015160 594622 934260 395912 287165 832833 082187 350057 917318 535557 623118 358289 190890 015052 773597 762934 182894 170924 131685 715454 420321 524941 915148 859433 781011 072820 839264 616001 109357 203842 299221 306319 564808 262285 969878 015789 838169 597025 686742 722954 087203 005711 904045 532878 425153 139710 218377 055302 695335 889273 027124 057700 930649 594526 797393 321708 881895 970310 186995 142763 362529 388730 795206 772869 349250 967457 823921 447659 312247 919721 728766 020723 654955 046016 492307 696149 748871 272818 641818 187055 388328 678101 379804 863063 924829 634141 346001 132835 216127 864188 755882 070541 752607 524100 703237 967589 730501 555235 904724 633530 001415 201300 238277 547642 273715 415549 298475 320777 751382 684152 212106 735551 879819 778087 383629 225744 947279 870028 563236 581430 048112 640599 371606 867554 732947 229337 613488 329970 595612 410656 442351 145846 234967 939497 863867 051380 831818 946230 532098 963002 340244 711865 368770 517152 091460 971796 402311 092082 330308 762559 579349 045773 544906 981586 203960 143730 902676 692668 264000 915011 742538 882641 461257 220342 213079 311441 737826 014614 381610 700785 450257 761481 339865 791637 154491 638632 544555 190257 580295 521217 426860 780358 841421 372123 339486 346152 058647 635836 664896 904976 000407 294378 624204 302941 562690 472539 138361 502842 157675 937973 225354 346918 388985 765270 671693 260628 317832 957813 761285 890210 782829 196016 538735 302738 398950 039257 147352 124882 237888 350005 369447 595743 110216 000026 504247 615153 470546 916679 319551 853772 462422 204773 373025 483231 307850 515364 955734 802613 273742 034920 619144 703841 240006 872418 190581 973140 868936 939856 245309 303511 828985 677126 699795 750278 654472 238278 840040 614757 456271 045516 383603 447558 872312 550133 066313 579734 845638 546018 885004 630158 910531 087169 909231 431963 047639 741022 565389 757856 964299 492390 347224 277665 628654 391356 094926 412827 464326 940852 259105 630432 697701 255438 377363 098912 755992 228074 750954 582706 129214 208653 800153 270012 560092 787718 358138 588255 189834 747506 181460 676960 011085 269129 995228 151059 090852 194017 835043 906952 207961 378172 428593 327626 804060 166436 289027 869687 991566 362366 159469 387671 460672 768265 550900 838863 874285 081149 684138 534396 400025 170316 288674 182925 455339 591935 007320 527820 660855 955839 815057 589535 977898 006167 667157 259987 754657 709236 076466 341467 379070 190857 873728 409644 468703 559240 987290 270231 806943 623295 847170 958117 186360 905361 031967 571445 030757 308427 357904 367671 792774 128608 934766 979323 944635 252352 355178 892188 999988 490564 883275 021467 410126 415612 345441 711028 705538 105214 380713 820685 613803 868826 087249 647523 158874 356906 846716 037522 676888 903526 644147 284112 325140 328360 275422 541497 242382 289446 765018 152594 671272 194512 174930 157582 906697 556480 578712 976708 834438 896047 712548 027487 362983 739941 911577 549222 801205 318255 972614 324209 095380 393427 734414 107603 853769 958191 981666 632934 388911 010818 541493 364377 280639 371715 397447 096817 099247 481670 064120 343038 954785 813377 449912 869347 496818 279473 881447 561043 087888 407038 509240 817687 401953 421338 038687 010595 139271 789813 664195 423180 421732 050436 425064 065241 547291 765082 904836 289690 203136 450966 944065 198842 993370 255411 867897 825613 499607 728033 200086 441257 276911 349544 348451 162655 963803 405197 152700 493284 944186 749672 031155 868394 499608 610137 749862 513658 584360 857639 420837 098750 752987 721393 266829 621706 583803 169499 171885 431835 795789 617081 008235 165376 759047 779489 736582 745860 028217 594625 920352 005210 030842 705625 070993 321357 659388 454827 465234 520579 068493 451910 086859 499274 475660 688588 989134 385245 857709 742409 399609 384873 256535 583431 706193 103684 601589 627335 561314 597801 587028 980338 307492 311716 334617 880288 522283 263146 311268 130087 421299 / 1499 > 813033 [i]
- extracting embedded OOA [i] would yield OA(813033, 3035, S81, 2997), but