Best Known (32, 32+∞, s)-Nets in Base 81
(32, 32+∞, 370)-Net over F81 — Constructive and digital
Digital (32, m, 370)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (32, 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
(32, 32+∞, 551)-Net over F81 — Digital
Digital (32, m, 551)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (32, 550)-sequence over F81, using
- t-expansion [i] based on digital (30, 550)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 30 and N(F) ≥ 551, using
- t-expansion [i] based on digital (30, 550)-sequence over F81, using
(32, 32+∞, 2706)-Net in Base 81 — Upper bound on s
There is no (32, m, 2707)-net in base 81 for arbitrarily large m, because
- m-reduction [i] would yield (32, 2705, 2707)-net in base 81, but
- extracting embedded OOA [i] would yield OA(812705, 2707, S81, 2673), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 389861 192622 413806 660279 047355 722661 263751 168203 981968 220981 483587 703482 742209 284500 884867 627617 434074 099163 709578 909555 205298 142193 143291 276048 405288 533171 003977 317021 847356 308843 926763 531874 763151 950290 555845 985035 099765 113293 286006 909667 622948 244275 301640 761030 299234 068638 585938 818604 422351 242908 942698 497630 121434 294282 574465 941819 312969 671319 404812 366649 193276 087300 553283 406894 313550 772634 342203 818098 267787 458238 673817 608388 119752 690636 275402 928664 547753 523792 891515 457734 536196 635913 377474 503968 432301 610735 529418 327147 855211 452771 569098 528650 932656 356165 510547 793217 018292 792799 985872 123745 070002 914119 633891 865070 948169 072481 336529 997420 136472 364091 829862 906390 471372 357302 744142 134254 859196 786573 541544 085150 600187 453932 424757 254426 779327 141246 748980 598161 299567 872903 946157 653463 295454 478374 882528 111874 689558 898779 014389 540231 732900 808579 897027 760804 543995 051060 801933 703245 527276 760713 265156 857904 445230 436986 015677 196364 041139 730281 649263 419809 431459 207131 742048 686520 829956 540720 214662 878735 590310 165927 814839 706677 857669 742535 062978 738409 445573 203365 333071 712737 846203 602561 064046 095216 303166 683215 746058 104946 032800 946281 409820 641658 326419 085553 851408 491428 912583 173450 295443 996483 234511 161235 772036 374757 412719 305547 634978 006902 388327 166265 911326 096645 942060 239056 524552 488790 612731 496366 523284 971693 482096 153100 807318 333016 863405 150947 708027 401162 814802 587865 880656 631184 438412 037962 713244 420404 194852 049538 527490 299663 264703 882864 655804 751599 747273 193394 416156 475261 413228 939139 204131 648133 116473 064071 183093 123320 969112 712345 878693 320516 113640 700425 714004 367950 357872 860714 917210 641388 949652 511639 841802 077323 348122 671266 913616 888727 385544 970951 588890 073774 775100 788547 513018 067476 041465 802465 692184 155147 226587 530825 108099 769169 690962 065871 054757 343335 651711 382208 773865 491597 254859 809710 902989 167160 957485 197679 489411 371581 027468 368242 706412 685900 160740 389091 807389 015736 997175 522389 139380 036962 892261 332609 979512 209398 043085 086308 506636 657366 584211 128010 810173 052656 306699 051565 992758 722453 911029 680071 595367 520005 930228 436552 736796 972342 778566 252990 522581 579038 472093 022167 703765 236053 054102 603334 171793 408563 010133 418397 581727 733218 798793 478168 124084 621893 652295 496181 775587 617460 581588 925029 348215 933734 211420 033677 270695 667844 632298 537301 913262 717521 311745 313121 442747 800844 727555 016493 043857 901070 899469 457017 234539 302706 292130 246196 476304 335808 912237 068970 067402 489966 297733 875349 410145 075727 030261 888190 560361 537311 143871 085107 310346 110194 920123 060129 095036 119992 729228 324598 139025 141817 912415 052705 825310 178285 999990 049168 538332 608467 974291 558157 584002 071287 843826 887844 948836 508563 800297 084962 644902 468744 478871 523480 481359 269328 383388 012365 901763 895644 215272 698149 095843 988960 010787 828871 875245 873536 975337 195476 472571 416906 276985 493269 033515 210476 644751 694526 424391 812628 700061 809207 270571 157406 044208 943393 439280 781353 342801 625355 362209 769686 224315 717973 399093 207337 698101 503392 502739 062978 617783 273927 207069 994153 653695 155873 748036 309109 707513 864885 939430 265912 801484 262144 263606 727800 454960 759235 983406 566590 077531 747710 848922 106631 216154 342979 020026 261187 539306 459725 293325 309261 376755 314330 045574 191041 321935 267692 774785 316410 559687 622171 968695 345493 806801 472876 322713 058723 958707 476393 494380 483500 580770 255007 294913 780211 254183 154255 423730 120205 988038 186957 996133 120713 009890 176967 559848 007882 111322 763563 598544 942666 741630 745648 558667 874021 294407 211985 254823 127973 064051 424522 766076 164841 023122 711295 332315 782561 421084 900491 096693 208446 470625 994924 482980 804985 745080 050543 873744 623154 992158 610702 477553 227627 584285 049838 494301 872705 337123 223348 846332 743036 968780 205701 124585 532242 049784 742487 847229 378317 928390 364384 482843 007849 628158 803704 530356 910824 146119 838710 902567 595338 188133 903459 645003 762765 593078 823855 705517 371460 605551 039772 433724 154755 866592 214132 646531 750506 763973 781345 517438 675441 842760 915850 787277 492616 561771 094925 415278 547706 474280 166619 561891 398890 184722 343809 304789 752755 411919 326599 625820 423682 392446 948934 522502 899997 008336 783291 857891 314283 585994 277177 411305 200023 575606 872842 870638 832798 413960 049586 903810 456513 302628 407191 314637 904479 380100 520003 709469 555456 211796 579720 769703 593426 582533 792856 487075 343477 121027 612463 658270 921909 171634 397626 164827 901101 598507 302365 499351 656250 082806 839213 792488 167677 412610 580230 932269 657851 832144 518356 661146 871566 885242 085269 469632 195346 520182 085114 244076 653934 634110 582550 491812 382305 608844 036502 795133 173692 501714 604940 967560 119889 526965 511719 597203 784276 015309 566520 035227 140166 780228 908797 986586 473809 103019 387806 746458 860183 727131 163820 907116 480959 697487 596350 343433 421318 949063 198167 216928 508739 025378 499004 800429 055490 893368 762093 443262 020781 966168 984938 840378 222452 704074 666468 035233 508677 706957 555230 181934 885512 746992 564017 233777 692946 686174 773622 955553 951945 351850 319387 245189 993559 762952 929901 725227 464232 446638 075506 991325 895496 842956 586755 463355 861070 324928 714439 251516 958580 307330 642475 708021 102174 803309 004340 169226 129924 821027 925791 491975 639701 992570 511869 396746 297100 095144 700447 122547 405535 343948 865055 133698 643700 895954 156189 117384 685597 544622 640519 166677 232945 565334 713118 725612 271063 311605 503792 210026 776317 592193 281227 318807 011516 672177 / 1337 > 812705 [i]
- extracting embedded OOA [i] would yield OA(812705, 2707, S81, 2673), but