MinT - Best Known (260−114, 260, s)-Nets in Base 4

Best Known (260−114, 260, s)-Nets in Base 4

(260−114, 260, 137)-Net over F₄ — Constructive and digital

Digital (146, 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]

(260−114, 260, 274)-Net over F₄ — Digital

Digital (146, 260, 274)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−114, 260, 4056)-Net in Base 4 — Upper bound on s

There is no (146, 260, 4057)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 465398 067731 418141 612583 025942 685151 892135 488988 111771 513961 811527 265460 051459 075131 823206 913235 542917 633863 217141 990051 371567 593406 648215 119360 132482 996760 > 4²⁶⁰ [i]