MinT - Best Known (148, 148+112, s)-Nets in Base 4

Best Known (148, 148+112, s)-Nets in Base 4

(148, 148+112, 137)-Net over F₄ — Constructive and digital

Digital (148, 260, 137)-net over F₄, using

t-expansion [i] based on digital (145, 260, 137)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 72, 33)-net over F₄, using
    - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
        an explicitly constructive algebraic function field [i]
  2. digital (73, 188, 104)-net over F₄, using
    - net from sequence [i] based on digital (73, 103)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
        F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(148, 148+112, 290)-Net over F₄ — Digital

Digital (148, 260, 290)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 148+112, 4470)-Net in Base 4 — Upper bound on s

There is no (148, 260, 4471)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 455077 359609 092454 716319 570770 518232 283120 077492 420975 248098 790758 892337 625026 290604 255220 007740 076216 861207 627827 795946 625660 601408 162377 059999 002509 826760 > 4²⁶⁰ [i]