Best Known (41, 41+∞, s)-Nets in Base 27
(41, 41+∞, 114)-Net over F27 — Constructive and digital
Digital (41, m, 114)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (41, 113)-sequence over F27, using
- t-expansion [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- t-expansion [i] based on digital (23, 113)-sequence over F27, using
(41, 41+∞, 273)-Net over F27 — Digital
Digital (41, m, 273)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (41, 272)-sequence over F27, using
- t-expansion [i] based on digital (40, 272)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 40 and N(F) ≥ 273, using
- t-expansion [i] based on digital (40, 272)-sequence over F27, using
(41, 41+∞, 1122)-Net in Base 27 — Upper bound on s
There is no (41, m, 1123)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (41, 2243, 1123)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(272243, 1123, S27, 2, 2202), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9269 546919 162512 163060 103517 598438 656182 396120 648581 620859 872701 365191 038719 684123 271325 711812 969240 335697 117764 031238 515446 888775 230190 631263 183295 145085 904151 470473 941651 206587 768727 409556 200153 208602 709330 247031 585760 667275 651491 550592 215358 340066 929055 933184 557766 235042 557125 212748 945448 272614 447502 576455 107409 469666 233140 852449 237353 729366 408622 955712 164869 573510 525850 127029 416736 446256 288060 162146 072013 052987 882007 718410 330099 870809 999829 415749 173811 054220 813756 481693 529565 601633 003449 889984 692283 912335 804551 712656 678732 254344 218408 806803 959980 120234 747277 772726 615143 571465 852122 857245 625823 108195 147326 012027 564256 151429 654927 969878 306959 952507 005381 470012 674284 581367 683125 896313 058061 047584 269809 407795 719003 671011 423818 967052 939024 018897 874064 564547 233024 999347 850276 773978 760468 084766 491078 552196 731451 180077 581706 623897 829993 461345 930537 626438 648074 728400 262932 904416 019636 817536 756679 724839 951251 511338 119262 953007 500561 388261 906973 577758 143325 370128 339062 987564 851085 141851 796627 481152 354560 601611 392822 912662 374463 885733 784846 100032 311255 373381 691551 622098 846152 597843 787699 046986 396524 957693 840576 632519 038890 629378 249854 435878 178909 623866 608428 456513 664394 634770 025021 714268 110698 051492 116874 376477 199353 774451 178419 080398 946034 861953 228451 461771 235999 730838 775924 637000 167785 170487 991599 732674 294802 158377 338700 141734 036033 495750 508375 715034 220925 854994 527240 386993 226426 493892 770041 747656 504032 679432 798099 716763 426246 725579 240943 406430 847659 134630 602851 633515 215633 378574 673943 739621 860830 193708 050543 424298 915957 355242 867548 734698 934671 561392 851088 344971 827906 685090 492796 049302 968300 425854 054457 913397 894842 389881 313679 410260 744681 227001 211709 022251 058912 918455 549127 325329 379256 224397 439682 309975 630857 747296 357335 440580 011618 178021 536125 912907 860217 674672 931413 500208 735600 827102 014795 673382 008051 713715 553423 862071 890954 039385 305972 028392 434730 801615 873376 500835 619064 947272 017962 634004 594668 200843 882666 081500 957835 275185 603612 068201 882399 097961 408937 074382 733435 495063 502166 555789 316334 503400 447817 077837 509938 578364 391466 609715 150190 335823 480480 711241 954201 126755 120892 782711 955371 606920 797272 710214 093541 549672 500020 369069 123142 215857 200927 660472 780858 733665 876563 922690 346306 465237 697532 478305 106350 231389 187063 694383 117997 598411 862532 686148 571176 464033 226028 609938 264154 515978 111795 893315 718598 982597 723705 991181 284504 195474 581768 257842 247785 503613 297924 175751 683409 496653 991894 131493 923793 531825 745490 834902 376805 010075 910582 722342 712914 807844 735717 162523 777715 787137 082095 363478 552943 380055 494629 969693 990427 686678 932585 187218 247687 679980 028725 827896 124375 800931 824077 706569 147426 373490 239131 793781 433846 591050 674466 408928 118948 150753 199595 106259 921832 663817 933909 193806 774213 084378 882250 743750 568872 800377 555908 321585 050386 198009 454218 161851 468262 994614 255657 091538 612811 399322 782105 399660 749132 852915 405540 810928 828187 691525 220619 769887 808043 971079 875572 217667 575954 586981 618142 358898 979983 090659 161760 212476 467024 757299 304805 049849 597372 036860 985720 036175 710438 346110 464198 600610 950815 888712 699313 229990 726783 050725 232177 110019 887168 969821 465378 666897 463136 005279 513682 081124 321629 166242 805838 497721 378105 557414 036914 938326 568552 019871 127906 343213 285615 619348 834231 626577 / 2203 > 272243 [i]
- extracting embedded OOA [i] would yield OOA(272243, 1123, S27, 2, 2202), but