Best Known (22, 22+∞, s)-Nets in Base 81
(22, 22+∞, 370)-Net over F81 — Constructive and digital
Digital (22, m, 370)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (22, 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
(22, 22+∞, 1886)-Net in Base 81 — Upper bound on s
There is no (22, m, 1887)-net in base 81 for arbitrarily large m, because
- m-reduction [i] would yield (22, 1885, 1887)-net in base 81, but
- extracting embedded OOA [i] would yield OA(811885, 1887, S81, 1863), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 758345 056186 778407 390631 981794 466188 559302 870326 501215 207285 390210 711819 956320 741082 477365 766941 437721 975000 235601 299195 656129 369844 172692 848507 814531 070405 734198 334144 136796 329101 927964 683393 797929 828375 893475 676871 274449 456914 199811 818445 335541 608351 219301 213006 949058 611862 001367 072409 489334 695844 984203 964364 686519 407254 861976 200697 232726 438048 969180 765533 703592 103304 107687 320822 334523 693000 316499 295755 553020 787121 627080 196967 343261 193007 480053 392367 265037 817459 991165 285024 894576 195629 924128 033640 908325 190343 922313 791667 700419 339994 349043 989863 616670 951066 292517 703696 413785 508966 104280 316507 249507 274759 738343 066018 349101 160949 022677 749795 862706 629128 536935 749165 618049 967433 981940 683628 045450 349188 231196 570228 026859 281732 323802 282835 549188 683414 546417 338433 176832 689455 815286 169309 757402 896308 421385 164658 383221 496921 236329 390787 345845 891453 128476 455097 297098 198443 445572 507500 858337 443070 733394 389627 991580 412569 720364 752717 931882 360140 958584 687428 226995 757674 888535 313153 913331 052846 825549 341399 294841 223240 915512 593774 865623 649318 813480 074172 081039 568552 010208 244049 563322 223044 723244 651018 699386 214765 255221 850345 068575 696126 678235 269666 969827 309971 675729 911651 260530 549000 371303 751575 188150 619008 621992 856141 149015 974843 656167 698562 767786 707723 219870 888313 371311 718219 285829 029995 633596 200882 492185 319900 703495 706744 006922 219310 285511 474482 079010 762761 493727 316567 722142 286360 029520 909526 060885 472818 629727 002899 482807 693429 819610 541664 786460 166154 564476 238244 256521 977037 030308 190249 409134 102469 696061 016349 343108 988903 526936 094412 545891 928684 040541 752738 264186 384630 517917 685812 313589 466631 552418 797919 573817 854470 164921 504488 532148 812723 648696 271557 200738 251458 364467 130220 520019 319024 573186 723906 044654 642961 338033 935038 639637 761597 857392 980696 123013 174754 914758 709383 723766 860287 140060 384897 170206 119581 121104 881520 800876 490112 972798 104078 531639 814166 250394 094225 638528 706588 599767 221882 103458 742428 760861 323237 014481 424772 422334 596870 819041 037663 770586 985911 343478 069306 781830 205727 925403 232585 712624 306788 461547 982465 841646 970277 195370 711037 209723 742193 801140 358930 846836 015165 242061 006845 554482 553683 456564 097342 062920 906022 538657 416223 991649 246340 095402 922468 254906 964057 903810 636826 783017 762292 266396 140319 910880 075153 499775 673065 302985 828347 131859 161100 072748 523756 455409 775940 134375 801596 352395 726632 058251 391536 613185 109246 046846 996005 286219 795279 569954 047677 948887 947130 660683 746139 897402 073061 330056 752822 601521 600593 597268 000992 323167 234761 898703 833190 210633 845216 783640 225638 411361 631970 155921 030833 372129 517963 527424 361284 337054 794921 272279 164077 405468 926413 771339 035099 715574 125825 081532 884526 123239 740337 768052 983367 582147 089820 296255 401028 410333 657255 885242 202365 941692 686804 734771 665503 569531 470478 343188 488388 669609 486856 115080 441238 339393 999181 521844 701445 683149 004207 264090 363480 117855 703450 918113 232605 405845 936902 251813 683785 978373 487203 065244 565562 428092 910668 881656 096121 460207 296987 964603 089571 463496 909995 562063 172479 275454 117614 165951 855563 452579 210810 150152 048230 936784 807687 902345 608497 330369 175482 314544 389692 665418 008401 638100 275642 775960 792450 387028 192515 010127 790200 292069 648371 137635 973804 446184 130891 922962 311068 242810 653101 169154 747198 273856 866189 164845 745901 863442 291259 312126 545462 096937 200671 116046 688531 193013 769358 376389 404018 115645 687585 497300 953594 182711 451032 865017 327967 775656 589136 367077 984478 141713 517764 839376 557015 127487 521771 932074 451628 882195 666909 497868 629010 554715 701704 990988 119958 079512 555753 827720 197391 989739 508600 843175 715787 353408 602635 023671 666370 504563 793488 112975 660008 476552 504614 765819 006215 232090 838353 926082 148643 / 233 > 811885 [i]
- extracting embedded OOA [i] would yield OA(811885, 1887, S81, 1863), but