Best Known (24, ∞, s)-Nets in Base 64
(24, ∞, 177)-Net over F64 — Constructive and digital
Digital (24, m, 177)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (24, 176)-sequence over F64, using
- t-expansion [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- t-expansion [i] based on digital (7, 176)-sequence over F64, using
(24, ∞, 342)-Net over F64 — Digital
Digital (24, m, 342)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (24, 341)-sequence over F64, using
- t-expansion [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
- t-expansion [i] based on digital (20, 341)-sequence over F64, using
(24, ∞, 1625)-Net in Base 64 — Upper bound on s
There is no (24, m, 1626)-net in base 64 for arbitrarily large m, because
- m-reduction [i] would yield (24, 1624, 1626)-net in base 64, but
- extracting embedded OOA [i] would yield OA(641624, 1626, S64, 1600), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 286 702230 554427 055460 044029 260899 038499 197117 036974 956161 234185 319099 386673 977880 298356 190974 624908 593354 248638 786513 965246 546352 890921 689586 431650 985529 558165 512472 001382 960058 494214 603479 767159 084586 293095 176584 917615 271843 394579 810247 629081 637145 340291 855336 224715 866153 374478 405757 556179 942929 907989 699710 070658 463872 862541 537664 813663 536605 086743 162173 357771 890336 807520 827500 003416 729758 861273 398922 375602 087500 760923 348328 114766 110741 576148 739923 882056 181672 175411 358677 011528 897937 957115 240598 277965 867245 902333 434479 979950 654320 865452 176518 962424 208605 008198 573512 559409 253118 796311 871485 227617 319177 283998 030268 301144 625340 255308 842913 977836 515126 759898 541829 040995 812583 134120 170425 273722 917445 157757 015993 615405 445438 064835 733385 846770 664056 644548 635012 465563 575887 936543 987371 653149 948269 508778 714818 777030 723304 064776 248559 913254 830719 192656 120177 178872 888893 632693 361045 358325 903162 491921 429085 296009 145660 843446 359666 693368 714273 244481 812259 259261 631069 175357 750013 456072 467848 724117 641938 790425 586835 393398 437778 615554 931778 591145 584267 713525 783315 349936 890035 421443 906086 165620 766819 400163 759086 254736 162650 499028 912086 420749 068404 020759 846858 375683 678278 613418 800078 106420 920380 750767 850988 100283 287755 911867 537775 340845 618594 015296 994850 009078 865129 633053 465215 902861 115115 705104 731616 816330 634324 785138 251732 741923 608012 305733 362597 162767 719141 013012 697939 369287 631549 075593 786755 941391 324527 751746 345034 614365 812137 883615 689557 368494 460327 025354 594718 766123 802522 016851 887669 089262 878535 722961 752760 643986 528733 489630 478154 751326 398757 379056 422566 191135 729419 626438 714131 576844 377372 091094 745134 929302 608748 819084 173311 016593 679880 987701 484759 756320 437273 229922 606001 316832 720031 862531 085115 865499 169244 408552 161115 607770 264465 706252 294623 574287 549281 728897 430055 508467 063658 896958 767793 245773 323266 289949 786907 490519 907446 855654 132522 910234 422554 343794 012180 153340 049603 698710 949947 583360 948832 313992 711239 261845 288447 684627 069563 536273 521682 586546 615233 913268 761916 701729 702031 291387 727333 485146 503683 717083 765311 089770 984065 521179 812546 010294 211286 556844 554567 752721 783304 004347 594843 204255 376663 095269 095627 759618 933839 243475 278139 334033 268461 024263 836920 875525 643720 897249 153697 492323 429471 567948 080063 239787 070067 677221 649934 922103 817942 435995 521679 003146 727165 388399 055837 971218 132077 509103 731033 064861 119587 300170 619973 306402 466408 262370 633416 810330 891647 075581 379399 039204 015199 649126 061049 604452 695794 729346 056663 263409 250144 263939 117341 629234 199342 556510 730020 236791 820693 929934 383659 664167 531760 852726 788579 980564 373996 815239 618392 081330 295038 143469 217020 624421 121026 470764 200526 754742 241136 219052 954717 543249 793936 663812 805726 704426 229904 369761 682899 000703 051203 447689 560114 149003 112494 887696 414878 454122 625146 054224 887204 820105 033678 212084 477822 398376 135994 460963 131329 046976 008539 126203 316539 917239 570266 476739 553027 123778 709417 863199 249989 617247 153138 673082 001327 620539 978713 914489 898282 857711 796224 / 1601 > 641624 [i]
- extracting embedded OOA [i] would yield OA(641624, 1626, S64, 1600), but