Best Known (75, ∞, s)-Nets in Base 27
(75, ∞, 324)-Net over F27 — Constructive and digital
Digital (75, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (75, 323)-sequence over F27, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- F4 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 72 and N(F) ≥ 324, using
- t-expansion [i] based on digital (72, 323)-sequence over F27, using
(75, ∞, 325)-Net over F27 — Digital
Digital (75, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (75, 324)-sequence over F27, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 48 and N(F) ≥ 325, using
- t-expansion [i] based on digital (48, 324)-sequence over F27, using
(75, ∞, 2009)-Net in Base 27 — Upper bound on s
There is no (75, m, 2010)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (75, 4017, 2010)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(274017, 2010, S27, 2, 3942), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 243737 148263 769831 335246 530729 544896 537090 617360 421091 905539 595932 251349 397067 476449 395053 205476 693061 849062 171578 531899 195178 762041 314617 108026 191657 098501 684390 634751 569308 068366 757835 504628 066688 121540 418411 781935 703647 429752 426586 876391 373462 559183 455343 467594 894163 959323 623491 893805 707447 105025 558852 174053 477894 681208 297245 997125 299745 000487 037427 315005 022091 493843 221837 865785 928978 400411 396806 639174 545059 462495 136681 863690 093822 420586 308756 859818 173802 146334 902509 927984 226136 083892 635990 449518 595980 056180 831038 158821 007582 009927 644339 158740 014256 724728 545933 732187 428811 059460 049252 127098 758673 405041 595313 124118 641983 267222 865076 887765 645813 970695 002101 007288 646066 559404 209575 123097 292748 279363 338399 580598 484937 370773 508271 239512 009882 521730 705563 897088 014466 604284 409393 651813 440639 351667 634818 433315 804412 778514 934066 597762 730978 589064 605615 253788 148543 317585 843050 774262 506349 210666 386215 791081 502716 637126 853087 930566 809767 257535 993350 350378 763520 551591 946965 448732 315939 955308 868554 680558 600619 723233 732616 354291 575794 219599 391955 138880 240448 228186 395299 805392 891941 687943 387352 475041 665046 763555 617490 792503 872082 216017 171913 798246 782244 377951 719047 303317 307890 964771 325247 686167 090205 351069 808164 444716 452437 394996 570097 984991 900172 133891 442324 261909 530894 535563 139968 372507 188322 991836 297860 294889 873906 965047 138613 113936 956173 617417 005892 135860 235570 202508 935562 201454 825386 906092 871079 526982 075535 406447 741947 187784 698283 066780 009248 391438 191631 561252 920299 263267 111503 422827 060635 083582 261494 139558 235137 632644 970910 736684 668421 375923 545372 621527 294654 423206 308166 262623 370558 415020 045663 352220 229996 983863 140972 255679 793246 562418 959806 403250 230669 209328 602479 828315 745849 381979 615420 320852 271902 810557 822721 331460 728847 623070 505173 838944 539927 714120 993250 257367 330267 826171 433128 893532 052433 165493 604446 111027 614302 136578 910613 497953 595285 577099 603953 712327 771535 674263 914987 378523 442651 705869 164752 247756 932793 589560 170835 544169 116358 329752 732284 487253 476140 840617 338951 455277 505197 316386 262173 005053 522290 330279 183608 237187 209056 841770 553340 490944 247338 355480 648331 669237 271096 898679 217638 735815 704073 693231 021916 238839 308706 300330 044489 001953 943525 570278 630565 854360 996243 430790 707708 218269 406820 965527 481615 158364 171956 199209 756146 968500 692238 484445 549913 921619 195008 786413 276606 443169 291824 920009 429759 904900 271649 861758 195057 694384 316245 158313 596901 401802 547754 764673 620312 228401 413016 511693 369898 112917 249482 512715 765490 219117 193037 132121 847341 321640 509642 679909 868636 770820 717871 751095 507273 338840 381884 125397 187385 233527 428431 699869 318462 359807 951000 976892 758270 822262 840326 711380 988266 593226 027983 067716 792365 584844 625815 742875 033907 579330 482129 598420 012296 593155 894353 092859 157526 011053 142904 666009 900215 679187 337703 432368 672902 377948 413361 741343 844997 422607 210949 121145 973187 894534 350159 907890 777035 169359 127355 736912 115234 912126 307689 747964 087851 065608 997119 568347 176528 604808 136462 326398 220745 867323 636388 244306 087667 283038 816684 343527 219931 730365 345527 601479 102166 150005 000538 282420 138604 865476 355635 903070 776728 789261 533121 163653 650429 957925 642555 777866 176136 636244 601832 624538 623159 013419 508620 774873 349128 219343 619900 912726 068861 435167 186563 331614 861063 464052 576641 658300 992569 204263 171489 956519 728865 554973 440697 336849 446821 579332 410614 975742 793137 957620 049061 328773 432082 898343 196989 224873 374146 810327 574123 780654 138126 360298 426417 126392 448719 321967 036636 477639 616867 570667 154145 103328 728738 175447 889335 564312 449034 247258 382978 770366 576289 419942 237037 107525 608481 747952 972674 654495 485954 400363 609609 062996 756663 814577 159378 337053 279536 545677 773584 222970 373882 057453 553530 624330 848001 486665 879377 309090 438700 812362 892908 826634 111157 666269 314360 224903 010108 381705 914302 230460 729085 511869 823518 484339 597039 222451 590899 763342 644253 146947 758129 145921 926787 353306 137388 047897 253603 563641 322929 342788 671251 075613 602816 813313 083114 187953 251436 008609 851414 836765 506560 015637 859401 470586 711711 666245 866802 813415 854974 564331 441611 366321 206266 587971 409035 477773 659152 056213 864480 036708 205765 587833 420385 826176 562566 340160 977393 878992 954257 374509 371043 018534 963814 205560 390179 846722 745803 057837 297322 300146 253331 258466 321267 454986 281353 696444 635230 416096 131023 365915 743474 746183 738389 930314 099685 167862 818654 085054 762356 359522 578122 075713 857573 453225 902580 335156 120349 932650 897144 157852 051583 966110 749609 361150 397350 326662 184436 847627 366909 111714 640737 344365 941219 057034 071227 988768 341758 603487 193563 836205 314687 070421 366357 726294 891418 207942 713981 183707 702788 974080 892024 494107 140296 963714 798622 861273 462624 827386 061803 875148 996039 683746 684088 887608 811204 663503 792365 140084 099367 373493 297464 884786 098124 765022 527688 386002 485319 350689 976677 898892 963831 493931 539498 138772 094102 238502 545595 589516 292773 994403 202242 755984 602441 843402 515124 403452 960191 506592 338833 149287 396847 582919 279623 171417 431844 738332 868204 726114 355759 681993 757514 621895 335859 074828 793356 836971 546500 634171 685511 504634 017153 499651 912594 041485 796511 591672 802399 527145 259544 873906 573259 535053 083844 003705 719318 013585 980421 449391 103869 087019 013456 708216 275928 911615 284854 263319 154329 939831 058576 045278 031144 904901 345500 078853 142032 758995 433861 459013 635131 879301 614267 912862 739382 922248 251068 102018 629062 727847 568947 975855 783067 906769 200568 252408 246560 929316 715307 531319 951362 573275 555858 092385 268410 191193 159562 768109 185288 151182 448370 977876 230160 297506 813882 436829 056345 215255 751396 897476 389889 271204 152714 795443 291616 119583 003268 264493 443653 740102 221550 987574 669304 788697 681075 332239 680487 550239 155986 902205 459447 241140 011969 921902 723682 758961 496452 564506 377941 410964 748312 947487 614166 103918 309390 504559 840400 945493 748430 413286 610185 116672 168924 493121 795094 246861 001136 164321 103925 637097 866132 388655 152629 315183 310065 435086 584081 559582 016300 791652 874843 / 3943 > 274017 [i]
- extracting embedded OOA [i] would yield OOA(274017, 2010, S27, 2, 3942), but