MinT - Best Known (203−58, 203, s)-Nets in Base 4

Best Known (203−58, 203, s)-Nets in Base 4

(203−58, 203, 531)-Net over F₄ — Constructive and digital

Digital (145, 203, 531)-net over F₄, using

4 times m-reduction [i] based on digital (145, 207, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 69, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(203−58, 203, 1034)-Net over F₄ — Digital

Digital (145, 203, 1034)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−58, 203, 63717)-Net in Base 4 — Upper bound on s

There is no (145, 203, 63718)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 165 293558 844317 881003 000823 228262 954781 632636 989633 884675 701369 771866 437286 317754 287992 853968 624857 654658 525890 912026 498468 > 4²⁰³ [i]