MinT - Best Known (109, 109+∞, s)-Nets in Base 3

Best Known (109, 109+∞, s)-Nets in Base 3

Digital (109, m, 74)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (109, 73)-sequence over F₃, using
- t-expansion [i] based on digital (107, 73)-sequence over F₃, using
  - base reduction for sequences [i] 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 (109, m, 104)-net over F₃ for arbitrarily large m, using

There is no (109, m, 232)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (109, 1153, 232)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹¹⁵³, 232, S₃, 5, 1044), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 15 095688 381708 796386 560235 348255 419371 483072 127603 139046 925002 079760 169979 174566 372980 627074 130913 390773 677946 556434 469321 130771 891709 488478 691755 026484 921094 585577 312702 421285 634451 645678 772065 921493 254054 166031 681353 146936 340838 709944 309242 112379 238046 612951 464984 593801 647284 685196 126734 190888 896483 391689 028399 611014 048909 945934 337653 289334 158709 645601 397634 236522 079853 787385 155913 183998 049928 704764 334104 640291 078042 505497 375665 731543 447928 834946 749828 635846 005924 901481 829226 682839 148122 145082 941081 942181 558369 948850 159346 353695 940123 584573 292389 / 1045 > 3¹¹⁵³ [i]