Best Known (21, 21+∞, s)-Nets in Base 81
(21, 21+∞, 370)-Net over F81 — Constructive and digital
Digital (21, m, 370)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (21, 369)-sequence over F81, using
- t-expansion [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- t-expansion [i] based on digital (16, 369)-sequence over F81, using
(21, 21+∞, 1804)-Net in Base 81 — Upper bound on s
There is no (21, m, 1805)-net in base 81 for arbitrarily large m, because
- m-reduction [i] would yield (21, 1803, 1805)-net in base 81, but
- extracting embedded OOA [i] would yield OA(811803, 1805, S81, 1782), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 856529 665028 374853 495919 245655 051102 385425 283446 336710 829971 547303 569266 028334 569930 446207 076780 379991 029552 312034 685399 498345 429018 717110 400804 161415 953988 532274 862909 071337 330700 770731 050758 202213 643958 615319 729656 653728 366075 249648 459850 418487 437241 589465 125441 503456 141084 201340 574871 743880 541846 839291 923096 768315 227267 969837 943322 637871 931664 484359 453544 205883 321828 297643 176963 855394 246736 692087 690047 380019 129761 874989 921256 675994 285250 675062 365789 796357 139294 549592 281333 603981 263670 186836 317590 730216 661980 120142 142698 896232 090281 590427 829254 775064 919913 160687 697765 282025 428130 283515 207017 319482 442857 164521 201751 301484 243436 606059 115886 929720 584187 220449 043830 343018 100258 412398 406435 183626 609361 014734 219456 106153 600525 244115 109693 377287 196933 363327 373013 748528 415855 712271 601402 825828 746189 361667 973775 393186 969176 164616 452324 269876 972636 821710 565427 491760 000654 070033 974343 650512 271521 479701 918785 190318 752213 129288 548050 859862 524631 601386 146131 248242 845814 832066 739336 312985 438150 611422 130357 854671 460075 713902 562269 133914 899907 189806 089037 455478 838462 218128 241219 900233 536477 141659 928296 815114 600589 904364 118181 684667 638068 909368 528315 162493 361184 710427 605554 259668 404661 338685 962476 181858 762927 423304 108539 399441 598181 805782 385829 283425 986387 385723 121363 295786 448574 173983 360335 104911 613966 924193 644111 999663 575766 204013 526600 338215 195105 333741 919302 796333 925897 603307 626220 071994 366160 870948 860190 362330 743768 030536 735856 839829 412740 529886 328232 378213 378048 727273 189144 882550 784773 592061 436062 872255 869768 798340 813195 329792 034247 202757 363622 782671 526015 789973 083085 982951 623429 250511 142451 822110 084221 287582 991128 238181 288300 239658 617044 340041 421995 846505 016584 568861 139817 869506 698380 270541 657332 560217 427694 186425 386978 598379 256549 643839 831691 142034 018763 779280 032647 161327 282045 519755 103656 860698 649439 740564 183019 080421 347851 337226 095038 200613 166351 369535 041596 991092 881938 875290 222256 570074 771029 150719 661826 876501 182230 739862 812093 650851 760743 589120 644835 838441 997522 229580 720235 809547 166578 023248 778038 499976 436215 803960 250155 816245 998185 022114 531764 528548 546206 183075 430598 835112 044033 781501 688531 609779 727966 646304 397620 203600 172198 303581 591543 331908 139462 981866 496359 419176 081032 849304 257160 321804 129961 976298 780053 234382 834760 801439 970504 693986 881558 008833 524368 404084 698541 695315 790941 090065 642630 921254 609737 346512 009632 246868 338761 100298 186081 778887 817541 382607 142374 182846 317854 223298 000476 727856 478304 010641 246249 832477 596335 487650 721122 620552 647073 627280 849262 914612 182339 804590 688239 206944 380089 386453 583206 844815 186958 512951 402304 129990 234953 204912 124738 526001 621495 836826 445578 051209 488658 493860 401270 795856 274831 326805 488062 767657 738523 817225 438802 901012 008129 611607 328771 852458 608531 709586 589141 042350 450186 980183 629353 619536 868003 230839 612461 447025 305771 964002 092565 608856 209044 735607 898127 496312 284894 387686 343648 885660 444726 610115 736460 381685 852893 378233 047160 451571 965658 404636 481927 428336 489432 378259 021223 910821 835361 996853 196118 364533 947485 708238 111185 690933 994149 085270 291092 755297 280991 664072 486869 982509 413637 630866 830062 163940 150157 554701 483371 192454 706588 523967 199806 389376 449302 670670 264578 873118 637421 750258 231392 556012 083811 779795 771538 363792 775906 051511 449462 803020 739280 552533 996193 811207 627297 741103 561048 548658 650990 152189 507351 058415 631099 662335 401675 720365 357500 198713 961260 425982 780616 556246 599697 769940 553310 006529 445139 656897 125064 293729 791420 029559 420221 339157 543174 431181 546583 / 1783 > 811803 [i]
- extracting embedded OOA [i] would yield OA(811803, 1805, S81, 1782), but