Best Known (38, 38+∞, s)-Nets in Base 81
(38, 38+∞, 730)-Net over F81 — Constructive and digital
Digital (38, m, 730)-net over F81 for arbitrarily large m, using
- net from sequence [i] based on digital (38, 729)-sequence over F81, using
- t-expansion [i] based on digital (36, 729)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- the Hermitian function field over F81 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- t-expansion [i] based on digital (36, 729)-sequence over F81, using
(38, 38+∞, 3198)-Net in Base 81 — Upper bound on s
There is no (38, m, 3199)-net in base 81 for arbitrarily large m, because
- m-reduction [i] would yield (38, 3197, 3199)-net in base 81, but
- extracting embedded OOA [i] would yield OA(813197, 3199, S81, 3159), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 21 631686 185378 154978 476388 582827 765674 576059 701983 466229 664591 379283 763381 666680 052980 212885 132475 659191 496418 873934 653424 279308 211283 161415 796689 473979 945355 010404 625711 150030 057476 201761 135575 139793 534771 228141 479510 258326 504772 358344 833724 110184 314691 132672 469073 780551 993085 051689 881571 906406 405107 247443 906262 360107 661145 299439 192316 721122 514501 262968 990164 348921 194890 036389 778832 394944 298356 394116 711396 568248 596193 694530 768333 327219 824378 792883 839851 313499 623418 505552 646392 222611 381213 916865 492412 241507 427062 072026 469439 232416 295010 114980 264786 987304 642812 489950 392973 028887 190614 504573 118182 359957 972795 798855 048014 651048 206749 022951 127758 609460 152377 320484 333965 346518 241533 341637 135615 231989 547592 699357 104582 739827 200537 467067 005107 030692 210303 045303 442395 274412 527940 079460 863315 538301 032902 918766 029872 982125 072853 731383 172000 175949 928299 308189 520406 360420 118277 737437 994649 606002 359633 345114 141333 276414 161319 849100 515879 801777 526225 622311 564245 641063 888655 349531 299776 269962 528961 113329 105149 171877 804971 828501 649427 701348 017023 604894 729993 121010 150125 808137 273659 887606 081002 613181 746898 219425 655885 726391 419504 700391 663462 400838 777649 303296 322505 598321 645881 509410 308414 539593 705678 281645 059644 273420 865229 061724 013637 930187 168188 469419 780063 870285 205636 231318 159533 277078 483647 440714 702354 800985 667793 783117 640536 722456 751138 850568 061692 162867 738429 594206 461258 299907 780183 772462 534883 883521 167437 270094 498461 758647 219123 423529 589712 095947 167386 228575 508370 700000 152366 496448 850586 753648 502632 524107 509562 522352 631565 351520 296295 891167 951600 499927 376267 764919 295693 384843 087738 842412 626152 313580 480692 107281 954868 670207 949798 364103 878136 913039 910551 608169 723681 931500 435364 344203 008692 963287 589798 863509 342059 091129 841063 716829 337789 665469 667874 282690 370174 643067 966297 897816 613435 022488 807407 064065 561775 155031 286557 895658 289502 465588 917056 983247 391886 420134 687660 441218 220634 986043 388942 946663 759318 028848 228717 675640 978126 919997 752193 124228 999383 621151 359519 180597 657404 209683 802938 653680 206069 789714 307694 503650 162923 190759 610497 345794 378867 793639 615190 639422 529161 478659 802688 610526 146080 962163 346321 951167 870789 681561 858250 388728 482444 571671 926035 464085 139136 702436 219884 752572 163682 005954 421212 547252 721057 698348 184674 225324 759179 399624 258244 365507 455009 259259 251683 728902 168154 383687 571209 840567 539765 860029 849563 896031 306131 023796 890084 846147 765188 707440 241986 549680 755199 772825 604399 981277 698401 157808 481868 730495 380023 846835 296809 502083 522566 754113 915150 892711 755664 276922 123233 123771 375167 561894 294768 158442 130504 740807 810127 754382 872142 153465 596406 036421 941507 792541 519270 079244 885806 464087 864012 087900 422420 687153 585708 135787 920203 844892 375587 706347 608799 430309 377367 011339 685255 943157 046101 810857 269791 156051 061117 161184 815394 545708 442693 468240 221120 815456 828017 343415 968378 365034 432298 616047 851267 551590 599850 191749 366624 506616 538301 744899 023361 363103 733249 355780 505882 155012 859992 046556 596690 623542 736093 823462 418375 819100 307167 889892 670537 505406 227734 772870 134014 388374 712151 446763 900734 544403 294675 172884 511487 086811 112647 081028 183693 346628 993002 050800 484141 121712 144724 443146 008678 921350 604259 483551 684723 094915 932995 852988 866910 935222 988883 108886 028011 198556 985026 219698 815796 643907 890626 853690 686219 334536 516397 798330 704152 955902 420228 623770 602909 310546 741142 227942 866242 973809 397457 258146 128741 196912 954648 337978 537133 088692 165730 251113 299538 738512 713986 709180 176480 947154 137584 282005 998601 326331 744010 826457 027990 030854 266249 695671 876146 065053 653772 842276 573859 659608 128936 677383 200805 853991 328925 002290 959242 360431 392310 229986 789087 627340 871578 785961 131907 726089 962614 597974 900077 401670 865963 539935 996707 138558 992031 221906 358861 497274 397619 873561 272096 607249 835149 034043 489017 536479 665042 137076 011489 089806 664410 751327 126352 453360 307467 908600 976429 531111 603623 488104 246354 647935 561218 424313 686657 940841 930645 855126 900758 578324 474013 744371 845209 971895 579860 944515 512950 410989 256664 055083 236018 901674 769313 141928 343207 402225 160425 016617 591471 488427 064634 455152 586640 508799 607448 070905 306188 935544 933074 377921 141665 199127 669409 162055 998625 761698 036365 986642 679871 631570 693795 737662 519067 269697 502481 000166 719962 646411 906194 269211 655186 669037 824406 628568 979308 549628 011292 920390 605642 971481 376750 751708 384272 487609 358034 641101 345669 431122 382360 834184 393735 812590 983083 373121 627950 799024 178726 482351 747617 964301 492530 493972 953015 862963 527211 047618 924412 045483 066047 614871 205225 028597 832162 212305 116220 362481 301969 072440 949467 857195 109441 471894 406623 643981 316051 800878 102471 569636 607285 793625 900029 628687 337661 759303 325213 275359 097214 522861 157204 893528 300185 051125 117218 556853 826182 602248 750210 155053 886461 328362 917593 807528 497941 876636 298352 651595 353995 298233 231995 133480 629510 643924 837738 968414 669486 626412 960806 697662 645655 250691 393976 512122 376869 784020 773214 146644 806962 605898 071309 931258 958915 397648 727350 512206 327392 608822 135342 815689 123029 072175 229910 317073 194941 902613 032635 269143 130410 616262 370818 379476 375743 318990 664785 201276 670123 955656 883762 860128 313560 072769 271745 815880 145513 988234 322958 523153 388362 621743 301842 784311 896769 512557 307016 311843 951556 708300 172551 419691 688623 207925 713734 590004 837913 169506 537634 420614 837199 475530 750826 839221 111069 318225 662134 717348 077015 125485 177058 953995 800203 212746 714738 727945 789306 786539 377347 130104 658380 199565 667946 486886 223125 695457 669284 312878 268391 302350 278982 414119 398854 066249 102048 523404 604935 968409 567501 962445 191862 880766 743547 002174 699002 336889 962875 881803 654658 760969 986650 758529 582802 749938 580146 583652 858491 061428 362677 695694 312333 296655 781071 857891 483179 940334 094268 900309 348913 814898 768055 506311 196429 751153 556439 497917 559183 544645 106675 697600 889121 434635 741105 590444 327508 277741 938234 787148 745091 718543 840205 254365 488541 890063 227776 995539 205318 299205 267937 624150 976454 913023 576438 045279 090779 661276 880993 816142 525095 976118 692034 043009 355845 716257 239582 285970 069576 353250 064307 124507 682900 197490 960967 483918 582819 610513 925347 856040 483476 583856 999163 770275 770095 612759 671777 398764 071144 708435 827656 657786 653948 356940 421632 297298 987901 551069 076306 625013 284217 453460 323493 928102 886331 886757 968433 427041 / 79 > 813197 [i]
- extracting embedded OOA [i] would yield OA(813197, 3199, S81, 3159), but