MinT - Best Known (47−24, 47, s)-Nets in Base 4

Best Known (47−24, 47, s)-Nets in Base 4

(47−24, 47, 36)-Net over F₄ — Constructive and digital

Digital (23, 47, 36)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (4, 16, 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, 31, 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]

(47−24, 47, 45)-Net over F₄ — Digital

Digital (23, 47, 45)-net over F₄, using

net from sequence [i] based on digital (23, 44)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 23 and N(F) ≥ 45, using
  - a curve from the manYPoints database [i]

(47−24, 47, 392)-Net in Base 4 — Upper bound on s

There is no (23, 47, 393)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 20007 177761 725846 288972 444000 > 4⁴⁷ [i]