MinT - Best Known (41−20, 41, s)-Nets in Base 4

Best Known (41−20, 41, s)-Nets in Base 4

(41−20, 41, 36)-Net over F₄ — Constructive and digital

Digital (21, 41, 36)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (4, 14, 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, 27, 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]

(41−20, 41, 47)-Net over F₄ — Digital

Digital (21, 41, 47)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(41−20, 41, 436)-Net in Base 4 — Upper bound on s

There is no (21, 41, 437)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 4 930574 081043 855696 931708 > 4⁴¹ [i]