MinT - Best Known (79, ∞, s)-Nets in Base 4

Best Known (79, ∞, s)-Nets in Base 4

Digital (79, m, 104)-net over F₄ for arbitrarily large m, using

net from sequence [i] based on digital (79, 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 (79, m, 112)-net over F₄ for arbitrarily large m, using

net from sequence [i] based on digital (79, 111)-sequence over F₄, using
- t-expansion [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

There is no (79, m, 253)-net in base 4 for arbitrarily large m, because

m-reduction [i] would yield (79, 1007, 253)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4¹⁰⁰⁷, 253, S₄, 4, 928), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 1933 768056 409184 093653 159986 480180 559175 585952 148977 526523 521816 095764 835059 886788 844987 927647 630861 068144 560781 523536 660240 200977 231414 690948 476820 093861 027155 568702 937186 694606 160936 376578 312238 349302 919745 763076 268043 413561 134909 650401 734977 116764 276168 072589 982858 864149 778179 371243 531848 529021 919264 709374 863580 135806 464151 488272 507464 131381 837008 772153 586364 815955 620276 213513 238891 199374 678164 276648 079642 911012 201732 336753 694397 895951 521916 256818 594633 326499 110856 319470 515916 907548 705074 319180 964349 173761 152515 492127 579163 462074 944141 779039 540652 938817 103581 116536 723879 829282 283946 426060 016820 682752 / 929 > 4¹⁰⁰⁷ [i]