MinT - Best Known (22, 22+52, s)-Nets in Base 4

Best Known (22, 22+52, s)-Nets in Base 4

(22, 22+52, 34)-Net over F₄ — Constructive and digital

Digital (22, 74, 34)-net over F₄, using

t-expansion [i] based on digital (21, 74, 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+52, 44)-Net over F₄ — Digital

Digital (22, 74, 44)-net over F₄, using

t-expansion [i] based on digital (21, 74, 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+52, 126)-Net in Base 4 — Upper bound on s

There is no (22, 74, 127)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁷⁴, 127, S₄, 52), but
- the linear programming bound shows that MÂ â‰¥ 922 917897 581522 200478 159856 052816 460713 721200 165122 126976 779876 247942 380713 216692 127865 653550 855824 416202 838373 302272 / 2 456802 376692 185301 038512 138789 948002 484867 813738 396418 422046 677846 571469 > 4⁷⁴ [i]