Best Known (74, ∞, s)-Nets in Base 27
(74, ∞, 324)-Net over F27 — Constructive and digital
Digital (74, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (74, 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
(74, ∞, 325)-Net over F27 — Digital
Digital (74, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (74, 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
(74, ∞, 1983)-Net in Base 27 — Upper bound on s
There is no (74, m, 1984)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (74, 3965, 1984)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(273965, 1984, S27, 2, 3891), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 227 452324 003632 028712 124808 026152 869435 424700 465707 938824 071007 334063 569495 475232 620080 505464 654700 036487 844251 984120 485531 230963 445381 792210 314357 570709 901777 556143 171827 330637 352453 624030 779515 588336 551487 706871 222930 646388 243925 606457 285551 681232 335965 214844 164456 662473 892863 952052 624101 655885 237230 592602 830406 848293 752183 724566 976375 508671 000013 907115 647089 149893 913412 815003 548187 096981 316686 713437 458766 605909 501627 710733 716847 599090 756164 128045 811212 738120 510165 907430 563438 896434 684814 101941 348012 471358 205500 361079 842248 609623 263788 867698 408673 794287 022980 909636 741559 824794 307520 272083 540419 129729 513058 544646 719804 196581 895643 495264 937012 072700 463770 557714 319751 822642 479215 813595 037209 421051 578280 871042 091302 286734 000996 461557 617691 652043 642106 991623 695753 593017 720974 932718 433619 947783 527917 536160 244297 725514 373885 491476 965629 437205 872660 752141 950546 013034 657550 235271 981509 196402 580718 263105 886377 196669 525628 580244 965982 241027 977650 021760 047009 545940 551772 601163 077134 755078 756855 213168 436834 132723 984282 579557 860484 804354 957531 027644 618357 529657 050303 510370 741631 252382 204235 370127 050389 608935 243616 244460 230812 360223 412664 164503 424380 449032 855979 083546 438393 905342 036643 831034 168464 435704 958012 944534 320022 604456 933475 501804 520911 337761 798930 585941 144757 676942 842569 669976 406596 811572 032188 696100 144695 240812 950131 125503 434096 539609 216591 391829 697760 278529 041127 507659 554861 694346 991105 981514 001732 850187 099585 846787 028495 639100 341937 153127 722758 434008 207434 343252 827015 255153 247341 958403 028526 156240 840372 171564 334925 018549 120945 803002 378525 433361 427931 058055 521060 787085 274476 919105 688905 663947 249429 182874 382620 187921 174588 655585 978734 036756 514892 847484 177004 561474 504975 461023 145484 953780 822334 261711 345581 274371 140487 497972 209950 023329 356581 344411 871708 775130 955717 684679 880032 807322 899127 619905 127538 800547 057231 304345 296064 185482 475741 029030 319843 846544 990189 249835 366491 910999 179540 577414 170756 142690 168302 040725 456387 726494 128178 193373 577942 250924 347180 611643 604929 454548 121249 922744 904164 228423 151148 458441 090306 062825 374698 847900 426517 186734 298838 578108 052923 465084 041565 814080 522476 002444 108126 225348 640731 589378 921726 544688 377387 691510 175600 627898 361388 903609 252245 700668 224780 534930 413402 326069 259895 162482 261588 798460 698608 089101 168119 026426 384879 018672 030354 336405 784502 780857 701308 081804 906255 153222 527891 416421 557629 810951 105273 841936 511999 636464 884494 364663 351444 936856 473596 259055 398829 796291 530435 445845 061250 618621 643368 236392 720333 372646 167045 950998 691537 648744 965895 583887 926154 811783 929978 139371 432353 987661 674953 617300 770376 548689 078605 963080 248367 564556 643244 000292 098653 235508 118027 544170 675411 002901 954494 587331 858584 160472 826975 831853 876203 220044 816375 331175 440630 403091 418288 813695 549510 307514 386718 389490 516537 210265 857997 096310 216854 373179 965764 083576 970651 528715 209833 023316 346348 866069 950955 407654 965835 487943 206277 935087 280678 179513 434056 203957 268351 572121 388386 111369 763822 452104 466801 845576 749179 029998 118734 154015 269079 772154 396713 945636 366934 587231 212556 740031 615598 682929 982868 194613 143606 366790 434314 653809 606635 186258 146215 899589 943983 460365 106948 714110 762580 061194 659343 494120 613861 392352 860482 746816 888945 213629 027551 459650 179987 073356 310936 153687 068035 349018 461882 475331 341561 769826 957068 950389 783924 381071 167826 044225 970969 439503 367767 088072 190724 561304 081855 248551 451890 414538 524649 870068 375747 320759 450743 233655 761008 868428 016523 438280 242016 212482 145340 773962 908134 631773 998466 173992 876733 396477 994063 633898 297920 194096 761741 355240 073854 437174 742705 425780 644865 033400 338750 027846 348386 371720 782711 739141 793261 851091 583740 688367 101724 889709 289849 571934 416496 249498 781617 813348 658938 806552 199477 326237 327741 396643 430849 871346 892885 772816 334975 240571 576639 770294 757183 031871 327988 806887 347308 826592 040537 487482 767570 100500 111095 306507 590807 965476 150828 446931 728369 678937 537593 758174 879549 609907 810176 310656 478402 065876 868693 412936 438538 622778 939034 352763 315055 841940 455906 966372 917632 543932 975006 524398 594724 194295 576539 108324 717642 439742 253324 058005 176561 272361 496142 308946 532225 732893 375557 476614 215514 291513 043517 958807 542335 013236 286151 749468 797665 324971 477341 459937 802293 206880 702195 966199 743935 987173 196359 757442 824960 765809 156267 747547 644302 788273 447845 089229 286805 115416 889332 048334 980464 467026 292489 271470 544257 380070 185574 996405 882450 431754 450148 535748 630255 745376 175711 304831 018114 572278 196194 867372 178893 781877 891424 493778 355829 575479 613667 399913 990718 671203 264226 465399 864518 646843 217932 963884 464388 852454 225863 346932 373677 075395 642031 755922 372419 517342 619466 544592 936935 356421 560206 733719 699528 132490 338529 729757 258070 846998 969307 272856 529081 678581 890077 374118 751776 549353 248465 411114 564551 663611 356341 589592 268845 063841 702771 938173 443536 696075 648448 376198 481161 074132 112113 292516 841215 912833 571978 883997 529401 303371 680566 160564 254916 972133 028095 934922 729516 506306 713953 108263 343252 005911 451636 031848 103738 170004 453829 287377 977318 438639 040044 186600 711161 434367 885212 159795 175167 402664 539596 752541 554187 773737 443952 636028 389678 873155 358994 804706 876570 258386 724329 068910 078374 031847 876561 584066 370075 384434 216809 381126 267724 864905 901342 376014 397728 734383 180447 740684 007124 631489 400338 789170 546569 914900 731512 991237 954861 976130 820348 106179 390587 262251 410069 270077 098156 301440 885407 572615 833674 077122 230338 226569 655353 770091 572095 724080 003699 968563 343182 788673 274405 664476 662452 680861 933429 877005 304340 431829 317911 513873 431713 084330 463864 119185 293808 171403 080640 415080 679941 273441 109022 789283 590418 043479 173417 266022 484195 614582 554790 754294 526956 784269 692361 859059 350134 114950 197178 360922 702954 276487 180960 142147 557049 252808 959542 269728 656899 506599 196869 762670 414963 067177 452749 458886 503318 546165 262893 / 973 > 273965 [i]
- extracting embedded OOA [i] would yield OOA(273965, 1984, S27, 2, 3891), but