Best Known (18, ∞, s)-Nets in Base 81
(18, ∞, 370)-Net over F81 — Constructive and digital
Digital (18, m, 370)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (18, 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
(18, ∞, 1558)-Net in Base 81 — Upper bound on s
There is no (18, m, 1559)-net in base 81 for arbitrarily large m, because
- m-reduction [i] would yield (18, 1557, 1559)-net in base 81, but
- extracting embedded OOA [i] would yield OA(811557, 1559, S81, 1539), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2628 206063 617565 928798 575183 587494 615710 414919 904455 306602 626912 681953 135101 350317 341832 410152 161099 553582 657909 828064 011660 483668 445152 449990 586945 477380 785953 215735 347818 307346 232396 149676 077835 509914 505357 485781 310884 080246 031415 847935 175819 740969 569053 157347 671125 665735 160585 327134 250730 885285 226586 916422 053764 909795 702134 244972 797388 066543 979460 249686 512810 099115 062012 067076 081496 492890 104839 828076 824592 430166 586092 933467 917215 825498 430161 600892 836897 834550 082392 191890 126630 694845 066679 340258 422277 460564 157114 076659 686674 557404 632308 781260 945394 922989 185059 236053 277194 226976 761294 519661 820134 924660 876648 802335 348520 934059 795347 593297 458752 590554 432031 134467 069033 388572 824189 373630 546534 903222 710281 752800 193260 934459 873251 004955 618211 491541 566448 965414 518695 505099 659264 953941 622924 649301 629063 947770 664373 354658 645867 701158 339967 540137 507208 134117 291642 547551 896437 369178 899564 842106 699484 428462 597009 877422 926188 690042 791334 826759 746105 446515 056583 904288 780062 388641 398141 695188 735021 911785 185310 017119 777316 965409 478830 219454 909356 137320 964333 885942 378686 283188 733460 607889 569341 405281 488969 009061 104021 498338 263350 827514 018450 278776 247172 776549 898243 069692 792059 772020 127116 606590 620013 874251 049452 883395 757977 896787 478981 073308 999020 646073 718069 167277 134890 958713 119714 780836 704087 451509 728807 140871 365664 444695 410085 055214 589768 359166 476844 047297 968453 943182 946121 531179 684674 900928 934180 248476 613646 035984 581074 387425 368813 432066 124707 241260 740642 963773 468163 433971 118902 698799 712897 461683 071345 375169 219581 007005 093283 426639 948450 817617 023176 870146 586283 693469 166110 942027 106907 165899 451406 916099 795436 195140 440102 545535 012833 446872 691679 980126 360708 398403 902020 668700 744773 207477 905233 321025 765117 418667 635979 796231 373349 096073 294223 797566 719982 287574 398411 066230 071212 903925 375889 347359 596844 343713 384909 491033 412436 198670 121400 589084 726218 010060 844944 454574 190550 401251 226226 493806 847643 452718 647521 031543 829321 214364 929559 488060 028187 805325 627367 869551 648361 752091 895865 448229 608144 017756 467503 503981 040779 396360 162555 118392 178393 730489 820880 360764 137172 815546 372334 286200 488302 250821 609886 871173 296233 773288 119081 353277 835988 504396 241782 777351 833890 422653 655941 563549 786617 078536 125979 519672 272388 990737 989465 826801 488273 441949 552168 238468 452400 418013 885461 851026 546342 411728 737781 989707 063877 150943 544297 764563 111595 510104 818184 485433 470145 967356 527426 397335 505815 369838 266483 158416 614576 165833 510760 401912 966195 474255 309393 194759 393171 065904 160718 467092 514984 126264 609255 565519 878764 156723 140494 713671 836538 624528 618972 073746 621630 621798 137428 875431 650466 086094 679860 518185 292571 017058 491338 875281 719074 465958 249293 718209 140550 912291 396963 855264 621796 910059 078425 240971 865887 281319 762722 464071 404495 591700 195985 585656 543123 253329 381470 447773 095332 703758 107759 019256 875861 241755 823466 496066 159163 926295 378865 489597 900669 528236 959445 571753 328577 537243 336770 559607 370050 770561 569782 944540 647693 457002 987136 282317 791417 515387 978502 089916 322568 975841 / 77 > 811557 [i]
- extracting embedded OOA [i] would yield OA(811557, 1559, S81, 1539), but