MinT - Best Known (22, 22+43, s)-Nets in Base 4

Best Known (22, 22+43, s)-Nets in Base 4

(22, 22+43, 34)-Net over F₄ — Constructive and digital

Digital (22, 65, 34)-net over F₄, using

t-expansion [i] based on digital (21, 65, 34)-net over F₄, using
- net from sequence [i] based on digital (21, 33)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
    - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(22, 22+43, 44)-Net over F₄ — Digital

Digital (22, 65, 44)-net over F₄, using

t-expansion [i] based on digital (21, 65, 44)-net over F₄, using
- net from sequence [i] based on digital (21, 43)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 44, using
    - a curve from the manYPoints database [i]

(22, 22+43, 173)-Net in Base 4 — Upper bound on s

There is no (22, 65, 174)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶⁵, 174, S₄, 43), but
- the linear programming bound shows that MÂ â‰¥ 2 356982 708196 944001 632405 639197 943867 825680 395816 503599 985988 433957 852565 175436 909425 167874 773494 005760 / 1698 395268 555289 237515 503113 977957 762702 705839 816361 669722 314819 > 4⁶⁵ [i]