MinT - Best Known (103, ∞, s)-Nets in Base 3

Best Known (103, ∞, s)-Nets in Base 3

Digital (103, m, 70)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (103, 69)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 69)-sequence over F₉, using
  - s-reduction based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

Digital (103, m, 104)-net over F₃ for arbitrarily large m, using

There is no (103, m, 220)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (103, 1093, 220)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁰⁹³, 220, S₃, 5, 990), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 372 928486 816579 556011 918601 118423 662097 376574 698916 590652 951925 484864 282149 564658 599626 735277 926677 071792 757612 956818 072405 441043 631314 508242 225009 024932 108659 319377 844721 707369 837732 774725 111457 224919 773553 771890 009465 654487 872813 974885 330386 574617 679828 775262 486848 319242 593022 297879 090687 645256 611613 645095 852075 723383 364700 091665 845938 908996 923452 669481 789915 650928 166053 745136 647169 633486 678282 836375 666618 231825 087112 492619 837653 897496 947250 901776 381293 164736 951281 558718 419339 998628 324663 593234 865575 390412 822155 410231 / 991 > 3¹⁰⁹³ [i]