MinT - Best Known (44−22, 44, s)-Nets in Base 4

Best Known (44−22, 44, s)-Nets in Base 4

(44−22, 44, 36)-Net over F₄ — Constructive and digital

Digital (22, 44, 36)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (4, 15, 15)-net over F₄, using
  - net from sequence [i] based on digital (4, 14)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
      - an explicitly constructive algebraic function field [i]
2. digital (7, 29, 21)-net over F₄, using
  - net from sequence [i] based on digital (7, 20)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
      - an explicitly constructive algebraic function field [i]

(44−22, 44, 45)-Net over F₄ — Digital

Digital (22, 44, 45)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(44−22, 44, 410)-Net in Base 4 — Upper bound on s

There is no (22, 44, 411)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 315 018607 246512 354779 432932 > 4⁴⁴ [i]