MinT - Best Known (48−24, 48, s)-Nets in Base 4

Best Known (48−24, 48, s)-Nets in Base 4

(48−24, 48, 38)-Net over F₄ — Constructive and digital

Digital (24, 48, 38)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (5, 17, 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, 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]

(48−24, 48, 49)-Net over F₄ — Digital

Digital (24, 48, 49)-net over F₄, using

net from sequence [i] based on digital (24, 48)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 24 and N(F) ≥ 49, using
  - a curve from the manYPoints database [i]

(48−24, 48, 441)-Net in Base 4 — Upper bound on s

There is no (24, 48, 442)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 79454 362252 554256 460115 168820 > 4⁴⁸ [i]