Best Known (13, ∞, s)-Nets in Base 64
(13, ∞, 177)-Net over F64 — Constructive and digital
Digital (13, m, 177)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (13, 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
(13, ∞, 257)-Net over F64 — Digital
Digital (13, m, 257)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (13, 256)-sequence over F64, using
- t-expansion [i] based on digital (12, 256)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 12 and N(F) ≥ 257, using
- t-expansion [i] based on digital (12, 256)-sequence over F64, using
(13, ∞, 910)-Net in Base 64 — Upper bound on s
There is no (13, m, 911)-net in base 64 for arbitrarily large m, because
- m-reduction [i] would yield (13, 909, 911)-net in base 64, but
- extracting embedded OOA [i] would yield OA(64909, 911, S64, 896), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 102549 986815 636271 267529 397025 712500 896895 052830 435391 348525 055016 404534 560528 617282 997928 083094 070546 966239 830351 341257 169184 581562 460293 427554 789090 873596 338147 661847 495109 720921 376630 996004 072427 728662 181204 115833 420527 806568 808428 486624 627018 204159 138046 656287 115259 925637 126812 473765 239358 746502 065556 815352 590885 906424 006115 707873 742230 784414 560750 144547 568683 288270 576943 849675 997287 255619 914290 267556 544794 526879 551004 233587 633557 837683 603495 967561 080784 355364 358674 179484 984689 324725 383113 237625 427923 311598 193509 979473 059821 404574 183939 377094 922395 089261 976247 332936 597602 549589 795158 384047 628338 495874 319532 091141 978607 473499 337337 391336 147466 715361 399117 691695 376833 429329 645789 741629 162239 663527 348465 917794 694950 377054 810005 025269 529421 615832 514914 599956 120080 930806 362889 554933 571742 815203 702298 182755 172945 911555 421500 736498 605448 523386 174361 476378 567635 156967 117699 801646 193683 625509 547543 756797 776190 958762 820310 604089 373878 709344 554078 052683 864896 074595 719052 027884 878038 661955 953564 127913 335225 669622 334833 257162 234641 065699 220723 715123 090563 510810 078343 742837 911816 954718 556396 638018 199423 417859 420731 354085 459345 742094 198810 820555 232960 247387 876882 894228 529242 597812 569147 784965 286154 725708 166436 444045 040690 849224 759797 828988 939916 165043 050044 011169 877863 717491 987662 517631 751883 805991 089182 640390 357382 742518 588665 285107 358851 608003 857362 652269 174766 042868 641816 581990 851784 705984 832661 493101 473207 596538 860311 581977 415354 107566 115074 190376 566927 616327 400414 666426 934180 029118 616802 452879 805730 302099 019467 864807 632424 726472 114995 940046 323654 139437 918304 684623 183939 370333 885403 915345 954582 603590 133670 616563 249452 154880 / 299 > 64909 [i]
- extracting embedded OOA [i] would yield OA(64909, 911, S64, 896), but