Best Known (19, ∞, s)-Nets in Base 64
(19, ∞, 177)-Net over F64 — Constructive and digital
Digital (19, m, 177)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (19, 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
(19, ∞, 315)-Net over F64 — Digital
Digital (19, m, 315)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (19, 314)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 19 and N(F) ≥ 315, using
(19, ∞, 1300)-Net in Base 64 — Upper bound on s
There is no (19, m, 1301)-net in base 64 for arbitrarily large m, because
- m-reduction [i] would yield (19, 1299, 1301)-net in base 64, but
- extracting embedded OOA [i] would yield OA(641299, 1301, S64, 1280), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 108 134973 725099 976511 101863 000649 693854 380126 994266 857346 073709 461050 575945 236130 135398 309000 658398 345491 415164 014725 816792 667128 889669 485936 189691 673459 283346 079252 629512 493131 887557 778161 348571 708863 555645 978645 637422 106778 297328 732930 132265 792548 116880 942766 517942 431563 524032 233016 619212 683481 553040 068478 915195 087539 313334 092183 047880 469456 719940 227833 332031 166694 291246 219639 249862 303087 383343 012041 072305 339437 794868 125662 204307 951702 757678 723397 526748 992643 372407 024005 182602 976512 277811 334250 457289 533086 475592 793918 218197 392133 477512 237288 405810 849198 672272 539771 709733 658309 165463 720571 467965 388294 301044 634677 831290 983065 368384 572340 304287 830572 500300 146750 529983 759645 153784 069545 591214 805663 731247 664935 922641 748126 482511 977057 615753 737813 037708 406456 520183 436497 441790 511520 809387 108052 385188 905030 932819 402523 358769 727096 324685 667901 101402 166173 284842 974956 658841 968761 948647 061778 796562 155885 882690 515701 958646 241038 292538 042107 644758 823289 523060 803101 472455 594790 180255 876687 211279 441265 091200 349723 055009 349658 608626 498219 567903 662608 303442 507096 832915 112155 070715 245011 601706 076530 746669 748076 768166 894814 097801 581427 539263 204668 860207 274476 097263 503600 958476 222647 076166 248359 575439 063553 587677 548968 013905 738382 248010 209206 981842 811733 833515 084931 491568 509424 582136 822037 647406 200360 037183 962557 817784 301261 881321 582896 762840 301410 532640 684952 963781 866951 493829 380441 575540 830350 173209 036080 150658 569220 226040 308632 488617 528262 498387 093428 444174 488160 047171 089038 695547 395045 941608 945794 359920 245622 173389 508284 519262 079039 483023 885941 339762 464154 944309 702287 093784 351082 907543 863103 981266 039112 442314 106109 545158 288609 945012 610580 856135 926166 134957 661914 037788 520957 129077 575865 501958 994646 353876 448133 586900 568550 109539 373285 374828 600047 915304 047673 755807 557128 221016 796791 080674 628185 441687 966908 195677 782790 611061 647261 857715 436691 312562 737432 373334 582799 257817 084528 578589 714726 158132 027135 349393 016287 379815 855659 824155 355706 663204 892841 460024 002578 067969 422050 240715 970041 602615 168898 481513 700013 001472 991828 498948 895248 304842 718865 835560 499042 537630 915964 284162 584132 926903 406114 366855 630085 486768 283860 226028 856558 004386 834025 752867 212796 315867 215399 376967 378810 112947 935552 127827 765864 806619 965327 186199 227487 963804 143043 467165 293821 558771 981074 268471 889414 778713 022610 327753 599037 161009 377124 857865 964277 672890 597376 / 61 > 641299 [i]
- extracting embedded OOA [i] would yield OA(641299, 1301, S64, 1280), but