MinT - Best Known (26, 26+∞, s)-Nets in Base 4

Best Known (26, 26+∞, s)-Nets in Base 4

Digital (26, m, 34)-net over F₄ for arbitrarily large m, using

(26, m, 36)-net in base 4 for arbitrarily large m, using

net from sequence [i] based on (26, 35)-sequence in base 4, using
- base expansion [i] based on digital (52, 35)-sequence over F₂, using
  - t-expansion [i] based on digital (51, 35)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 41, N(F)Â =Â 32, 1 place with degree 2, and 3 places with degree 4 [i] based on function field F/F₂ with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]

Digital (26, m, 55)-net over F₄ for arbitrarily large m, using

There is no (26, m, 92)-net in base 4 for arbitrarily large m, because

m-reduction [i] would yield (26, 272, 92)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4²⁷², 92, S₄, 3, 246), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 921 377545 122446 619199 598286 374089 084696 513969 828232 526459 034741 270904 336521 520715 841339 532514 076847 544303 802497 745079 321233 052888 165232 576308 943909 041185 557531 590656 / 13 > 4²⁷² [i]