Best Known (16, ∞, s)-Nets in Base 32
(16, ∞, 120)-Net over F32 — Constructive and digital
Digital (16, m, 120)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (16, 119)-sequence over F32, using
- t-expansion [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- t-expansion [i] based on digital (11, 119)-sequence over F32, using
(16, ∞, 158)-Net over F32 — Digital
Digital (16, m, 158)-net over F32 for arbitrarily large m, using
- net from sequence [i] based on digital (16, 157)-sequence over F32, using
- t-expansion [i] based on digital (15, 157)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 15 and N(F) ≥ 158, using
- t-expansion [i] based on digital (15, 157)-sequence over F32, using
(16, ∞, 559)-Net in Base 32 — Upper bound on s
There is no (16, m, 560)-net in base 32 for arbitrarily large m, because
- m-reduction [i] would yield (16, 1117, 560)-net in base 32, but
- extracting embedded OOA [i] would yield OOA(321117, 560, S32, 2, 1101), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 13736 845172 797683 271589 055916 204747 839415 862257 041920 871243 972680 494788 004733 360576 762237 577837 548068 224997 028947 867682 427611 277569 083603 013069 130836 059787 798049 892565 375105 784215 428173 051313 691174 015918 495459 087385 389503 103534 518994 615352 068683 598693 417714 585910 190432 867929 541094 356862 920882 696616 198996 162690 785247 815362 540672 611367 841431 334008 432493 761089 756624 520997 769158 249149 564454 838819 283725 900588 206330 672629 324406 291007 738589 888016 434933 402842 738218 782778 486181 754741 973829 872946 271883 895812 782619 557253 494746 054634 514077 558692 000527 378432 796310 018763 101781 697724 810111 597346 790055 219912 664177 114269 179446 672916 542315 272028 855490 286841 105359 066059 787075 755891 172404 620760 307422 705648 537106 062483 268638 193326 559017 284405 398511 714386 211305 322079 550170 716111 684494 414304 849512 412632 147583 655639 046751 779756 693428 716601 831624 202737 417818 030921 105366 792720 383110 151512 209497 132335 174324 308667 006345 513734 655539 093277 998363 011753 276859 398938 848680 776623 623731 081481 174396 452885 121646 585256 253221 315820 331717 999674 263353 306475 063714 293214 782505 935989 024141 379726 556164 568975 415472 018930 995009 842743 625661 929051 428587 594699 409946 929086 582503 797920 316777 319944 096298 227170 434579 594678 775348 322472 382451 677257 962802 536659 257985 709804 154182 657221 928037 974744 595841 805851 392392 842870 069755 257485 268319 546057 543966 566052 305106 551938 655136 224892 794350 763977 036701 609629 233879 575437 511638 450011 527469 339884 418335 391330 147550 971070 737108 736333 624948 923762 231959 727404 093156 370019 723047 273074 270470 043018 452949 108062 101279 605106 205224 437866 763452 980464 791956 882567 188636 691189 884304 676215 864008 711102 279785 143629 151814 894007 029882 841661 664372 693441 576629 897409 550638 229924 901972 147884 261376 / 551 > 321117 [i]
- extracting embedded OOA [i] would yield OOA(321117, 560, S32, 2, 1101), but