Best Known (98, 98+∞, s)-Nets in Base 27
(98, 98+∞, 324)-Net over F27 — Constructive and digital
Digital (98, m, 324)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (98, 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
(98, 98+∞, 325)-Net over F27 — Digital
Digital (98, m, 325)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (98, 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
(98, 98+∞, 2610)-Net in Base 27 — Upper bound on s
There is no (98, m, 2611)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (98, 5219, 2611)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(275219, 2611, S27, 2, 5121), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 418 734647 071101 514612 134660 499719 311101 885698 769343 443740 688439 295368 717221 626001 042705 732262 320980 945290 163849 539981 348016 566840 941195 611925 048935 361152 221837 340641 623019 864104 582546 481498 795492 051058 931293 817702 538998 394631 506396 507165 039226 167978 383480 564557 142770 527713 943409 114115 322785 344877 999515 746408 915035 183538 789960 446016 044780 790004 810655 873073 427041 714054 838736 322510 798186 244111 624825 341911 447501 906605 607095 354326 854429 909985 964315 179749 607515 491429 787273 868965 292747 708964 611912 781892 072644 120648 369515 168048 916236 347886 179570 377662 806965 844189 904163 546610 880711 718929 596050 106810 100193 069910 518472 454419 205984 035875 561389 568906 776718 420072 212879 570511 903789 774880 331563 963766 937510 155856 266408 553972 322387 072223 315746 835293 780114 019368 913264 948406 423839 209069 372735 777593 755230 787978 444176 340983 270663 160446 589388 231904 585580 446988 943279 582496 502744 564972 803357 956779 734049 254232 882666 349459 391592 583468 560232 220543 307407 320207 192268 380137 159730 075560 626788 850607 442114 386995 704656 528549 550548 986121 865575 220409 826105 597353 487726 489072 651506 138994 978091 315703 406946 037280 767207 339932 905966 029680 737982 773022 266046 612048 382920 960208 033394 479585 374716 218868 519561 911650 492039 549546 428885 092969 092589 923817 145398 156597 221572 185297 444413 690816 716364 076975 317845 183694 478719 993238 668200 725931 445387 334112 247090 017611 844041 546408 812594 975988 817382 755108 184154 933861 210318 975257 856679 793964 740346 162436 578785 800552 137373 697574 268222 369441 595518 902818 524014 247050 377620 266692 191502 978409 260749 612216 946150 595002 728048 808385 107836 975997 537992 882839 197129 291607 851774 475958 657800 041364 093635 905068 100174 565729 954616 833494 714449 079885 039148 211168 724522 081249 322706 047315 734057 212624 480034 831742 627868 038145 419288 701438 803937 187155 829634 415619 538204 898546 400742 065040 569848 153671 169587 625938 695275 457242 896304 415085 200706 426748 521470 903656 768117 715271 388678 861101 772944 454842 805436 316479 371535 261713 653277 327262 996129 815249 633797 594971 227579 565970 029504 739978 353495 169306 525299 294633 290183 855529 153784 815478 103313 980387 280111 306670 718072 009049 472738 189010 109429 760549 974925 075058 458854 674701 787164 597694 980913 179991 760631 685058 492230 481516 840587 347985 420883 670373 365214 215654 924035 474172 095386 773164 419826 022182 439991 663177 402094 052434 239822 671087 753583 778151 267039 465318 630889 059903 441231 600169 340463 827135 530605 240861 184481 601613 605084 971613 564061 487387 314388 454617 266129 668475 005415 706546 820348 655355 893822 300931 536022 297871 889201 350753 391856 022284 180166 677033 887243 081083 526392 454008 565720 042575 885362 524089 498698 663427 460103 616600 662754 380802 976972 825439 943233 413962 937500 727446 413746 648201 282545 637769 773044 771238 841080 650288 781936 171372 063350 028893 404611 399313 348740 017108 683538 051879 954409 532080 431971 018590 807633 826086 323013 764316 972555 049542 489378 019332 983387 277156 213972 738342 599765 969656 273973 489996 273101 673508 957155 129486 307216 150578 533752 952878 384820 285955 708518 827170 647834 754600 785226 470562 167798 233870 753106 226232 076304 012622 221248 269675 205671 246800 405746 077236 337496 081795 627512 613173 763939 599634 039214 808701 908671 163302 953444 548191 602328 165952 423399 650488 936816 981721 026613 557874 746719 122365 343427 335860 889811 480582 834511 212775 807217 230606 758527 728993 745670 517379 182110 521159 445156 177730 509805 936880 973739 764062 828128 204464 046498 732261 927010 579579 420705 887155 693002 366399 141935 519796 613371 875242 463940 505516 674415 414116 963602 292465 232927 770186 582733 558116 749945 186828 063591 450457 310233 824528 780642 533516 666370 812366 292032 937564 639574 250334 778696 005503 280373 409205 095195 324324 011335 002958 415320 971738 931425 403057 256647 882775 940582 388361 523209 095399 597255 774481 835380 402663 259113 797157 245173 934655 410036 954056 281661 050845 658935 106214 360736 389751 870804 236330 697517 092800 417204 602600 133883 821535 688070 351415 704633 214577 873009 907341 316274 418593 776603 679904 842754 984314 571303 817645 574288 660797 706156 066825 957331 474730 218002 563330 379380 010334 900735 088740 492875 011663 770914 521494 199523 670675 557866 810488 341742 223034 169363 737509 069518 208545 472977 960443 422411 490030 052664 990777 311344 060265 162520 508166 816299 671284 804925 462941 446839 569820 010897 848446 774626 280380 872479 906948 562576 680361 125442 731715 420138 152659 108212 136560 107972 395205 364423 503195 693204 385608 841209 811657 772545 808535 262728 749337 149106 173983 075202 631755 749433 809437 171244 214363 600846 740346 301284 103564 732772 982190 209004 110909 280416 929404 353516 007767 261112 280160 519936 083662 252261 761497 171904 583939 700980 955527 856170 369157 429394 823142 536713 233681 271867 834156 674570 243958 579827 417196 046609 568361 238868 554256 402012 915130 903761 542425 575283 478363 353626 686030 928885 429375 126796 865544 912621 902965 301494 936134 869462 205373 397473 826130 831600 611638 220907 777709 413780 596874 983302 154637 175878 860097 452206 758059 007564 944599 417841 301949 946307 086191 619337 959782 595821 785493 517078 810311 127516 378627 792322 212350 972295 471843 365269 490918 661257 867812 261684 822518 957822 212103 286580 046935 662601 601838 111422 412942 973149 727651 372293 576231 207516 770993 930887 135210 154290 328709 664478 746015 644924 710456 634872 056113 928079 895645 599311 480207 724166 566430 900423 675741 078134 947358 757831 853801 315142 948647 387674 424161 847308 429375 102804 153169 171320 411567 297237 645657 322535 282315 779605 931640 122987 711201 570464 548779 009921 533348 963419 991876 840214 018554 283977 564168 764017 546120 961332 415468 211739 129019 104336 082337 071149 523006 425170 513828 801192 437839 163657 951476 685962 699002 435186 259129 894182 133744 180066 248160 592584 431061 568717 802137 717110 044190 978416 127656 207881 131525 509770 296060 978950 520271 267562 357994 956735 574736 895031 583580 722024 092692 533186 054321 043353 711721 231353 793037 581223 145386 181138 638557 456448 681156 293844 841311 290636 556063 899290 851148 702435 561434 279810 478819 866501 034642 445181 649144 010791 515734 954105 914722 735168 421854 500387 807121 127984 586531 598816 782023 199276 972754 330463 345867 860693 232875 537039 799961 213983 685191 412925 910531 165398 411467 233272 098869 485991 086339 586569 883944 359895 282672 862785 068212 655176 063420 745200 969931 772650 736052 548148 254875 162735 906823 330097 113983 654217 209589 289664 052216 466648 150332 216093 746324 921212 744734 705717 106715 914962 574141 183824 511678 256631 125986 533801 263580 988879 431213 937434 093635 316298 360633 994254 658171 815431 285831 605508 554702 382067 238840 173489 260350 004844 663908 964873 873331 831593 418647 163219 172162 723703 976730 115903 986113 149440 032687 874697 962384 559620 395689 021065 190322 417791 793739 163639 060243 030983 311649 468781 098166 199207 675526 120198 766150 716432 676961 301365 358045 961177 454126 139170 321614 600409 974828 299092 663447 515078 022374 039243 351850 025319 509089 996504 198793 482996 903160 974330 869917 546257 975210 384054 780020 276594 796883 860774 035038 698387 000511 356123 341057 233434 044986 662288 536789 678315 118502 723675 880782 747516 044622 242803 412359 532796 826908 015186 920763 066563 553579 641498 916132 687501 767859 486982 905086 177668 728051 253330 324310 475433 467001 597625 129581 031050 454153 138750 982246 835281 547733 868797 537242 394685 543858 842179 005930 196707 578839 115203 304066 283399 254035 487698 765267 465335 044021 488271 241563 041222 877107 295362 051554 396149 426284 775897 140154 707613 843043 394769 649575 758152 117286 315894 717760 488370 946106 023021 224699 567093 706069 789925 164320 156037 903264 341963 695465 182183 044408 396625 616363 696786 619165 861972 587876 331112 474234 433452 548911 044912 457703 364122 305401 185350 605426 883266 325216 535006 507751 714179 623686 624714 365983 389979 520806 131266 006806 421604 373783 389455 149879 489737 782096 293615 852792 944059 384573 397571 735039 091081 085242 276704 137438 558966 234963 366745 871087 980609 216633 426286 616409 939897 628289 113277 596757 334163 192428 118293 090738 203238 051968 853051 377199 351158 240242 442962 121608 / 197 > 275219 [i]
- extracting embedded OOA [i] would yield OOA(275219, 2611, S27, 2, 5121), but