MinT - Best Known (63, ∞, s)-Nets in Base 7

Best Known (63, ∞, s)-Nets in Base 7

Digital (63, m, 54)-net over F₇ for arbitrarily large m, using

net from sequence [i] based on digital (63, 53)-sequence over F₇, using
- t-expansion [i] based on digital (61, 53)-sequence over F₇, using
  - base reduction for sequences [i] based on digital (4, 53)-sequence over F₄₉, using
    - Niederreiter sequence [i]

Digital (63, m, 105)-net over F₇ for arbitrarily large m, using

There is no (63, m, 401)-net in base 7 for arbitrarily large m, because

m-reduction [i] would yield (63, 1199, 401)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7¹¹⁹⁹, 401, S₇, 3, 1136), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 95 712988 625312 458225 660571 363863 702498 779280 138376 430540 178342 382454 296177 009396 501289 154623 447137 193630 567701 539540 888530 900900 742233 298849 830807 546039 155626 389267 050781 304990 639738 976445 370004 536627 515217 264765 118174 160128 668427 995175 021487 691884 457178 956119 848433 633803 840632 178023 977004 906651 278649 900747 985275 191221 291532 122906 463252 589863 372903 789937 989779 888851 940830 140612 090169 575739 267665 794169 826577 164186 173284 397386 361326 736696 864759 226429 345454 006615 275857 899238 860364 790112 165275 667657 223109 834764 963967 161890 169429 559144 970437 432712 803696 365940 754709 289410 990348 527533 701918 952757 829370 044553 726668 755957 135944 580929 959587 430326 814605 427101 293285 414820 481792 168293 985307 913041 194323 939400 873450 857939 464937 594923 504727 009186 392004 658486 406569 786268 260138 847569 237222 629012 975014 050389 439569 702848 683431 461219 307297 782815 971741 254761 047660 730748 253160 473394 134053 150848 316206 443770 524276 141234 696916 231297 860279 584810 370484 525600 998815 779964 935546 470314 953210 602951 917041 863823 446366 890423 773780 560073 / 379 > 7¹¹⁹⁹ [i]