MinT - Best Known (23, 45, s)-Nets in Base 4

Best Known (23, 45, s)-Nets in Base 4

(23, 45, 38)-Net over F₄ — Constructive and digital

Digital (23, 45, 38)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (5, 16, 17)-net over F₄, using
  - net from sequence [i] based on digital (5, 16)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, 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]

(23, 45, 49)-Net over F₄ — Digital

Digital (23, 45, 49)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(23, 45, 466)-Net in Base 4 — Upper bound on s

There is no (23, 45, 467)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1249 946775 307445 695097 386360 > 4⁴⁵ [i]