MinT - Best Known (90, 90+∞, s)-Nets in Base 4

Best Known (90, 90+∞, s)-Nets in Base 4

Digital (90, m, 104)-net over F₄ for arbitrarily large m, using

net from sequence [i] based on digital (90, 103)-sequence over F₄, using
- t-expansion [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

Digital (90, m, 129)-net over F₄ for arbitrarily large m, using

net from sequence [i] based on digital (90, 128)-sequence over F₄, using
- t-expansion [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

There is no (90, m, 287)-net in base 4 for arbitrarily large m, because

m-reduction [i] would yield (90, 1142, 287)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4¹¹⁴², 287, S₄, 4, 1052), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 1 427480 182988 026974 627685 460486 725791 635867 623721 151683 558371 903882 894994 537025 514781 160144 860812 764883 690386 979597 813447 666427 858219 773967 330891 191875 670627 408813 418732 601999 930324 185431 399714 556399 580928 224893 850972 192997 615501 145903 610407 983573 635102 678394 012744 466808 307292 733348 918280 009818 974775 461446 991201 038665 629349 862735 731360 504412 437140 390865 605447 122960 400717 045854 737366 955436 687401 584801 822119 938306 363125 936939 781333 481103 459810 808385 941717 324359 008768 379426 357862 086036 733522 593327 085052 593236 999993 498171 933208 414703 758118 275076 437484 628095 677680 022255 734847 228147 395916 170859 319619 310932 782089 443366 588953 499818 417243 673377 410960 333397 814430 848549 645226 151738 025076 326400 / 351 > 4¹¹⁴² [i]