Best Known (164−97, 164, s)-Nets in Base 3
(164−97, 164, 48)-Net over F3 — Constructive and digital
Digital (67, 164, 48)-net over F3, using
- t-expansion [i] based on digital (45, 164, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(164−97, 164, 72)-Net over F3 — Digital
Digital (67, 164, 72)-net over F3, using
- net from sequence [i] based on digital (67, 71)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 67 and N(F) ≥ 72, using
(164−97, 164, 296)-Net in Base 3 — Upper bound on s
There is no (67, 164, 297)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(3164, 297, S3, 97), but
- 3 times code embedding in larger space [i] would yield OA(3167, 300, S3, 97), but
- the linear programming bound shows that M ≥ 3494 403345 163599 783625 766126 050834 389607 938204 618460 033553 980709 342582 564978 614083 451277 906376 788494 665102 827657 333231 776259 392689 684400 098013 033753 023738 148733 810400 712769 183974 972075 699024 315966 053932 699402 339817 612590 957606 645231 295450 589518 385003 245843 263698 910781 237178 614773 952890 074279 370589 497471 654103 171139 553719 563874 970360 327223 737229 755161 967665 962678 347051 289296 816691 753942 440286 394318 502549 047201 121420 162167 646994 590879 744987 227102 253206 962976 025839 133886 497633 698133 678995 770109 039165 775457 109997 797755 711404 040990 967307 866108 891667 439755 141413 163040 767227 443794 226224 286871 857753 722989 256252 111304 800242 233911 435154 190948 116735 145902 137905 232352 961327 176392 606270 395430 536007 643690 763346 659879 868335 387284 537987 293800 676548 002280 839012 061861 596688 009684 352026 501602 961753 506129 728203 721724 393173 938181 025827 705918 481255 255073 477448 343855 646747 342204 822431 416915 371463 415497 326599 168872 051488 770011 318329 323509 709739 920101 489948 529347 042082 906727 549720 750687 242760 823478 812060 635539 504536 363809 284826 856311 358571 / 40 329597 518918 731582 875888 765228 371548 792770 641820 171455 930159 447654 272051 487654 853259 477579 627712 938628 619376 241377 866094 993549 012558 846496 444754 165092 557644 612060 208549 571978 204039 170342 352367 879991 894034 717552 337297 776475 734852 098733 307224 076929 758204 922301 327157 277098 540272 092025 731523 575010 120097 008431 457499 828688 030390 600669 787536 163180 926751 288505 440724 371755 880042 928295 752161 795181 127494 053270 492621 106102 706296 709477 647435 375060 299987 968866 442685 248375 251400 200833 025415 585835 121172 822327 364328 727141 675665 604874 263792 758270 589882 831648 042799 569576 077959 674835 845932 563392 271838 381259 095797 949546 202314 178263 525518 342301 493722 253146 584577 143951 178079 040958 116885 028124 956154 451438 128115 170506 541229 228709 641565 861563 551160 768853 422629 683722 396542 059616 793102 991868 340430 140807 166267 481396 406542 812915 670452 203432 795497 740620 545477 028134 080937 475245 533709 646423 368455 569146 373129 542570 933441 926978 541040 313060 839756 283011 239930 757350 657732 > 3167 [i]
- 3 times code embedding in larger space [i] would yield OA(3167, 300, S3, 97), but