MinT - Best Known (260−110, 260, s)-Nets in Base 4

Best Known (260−110, 260, s)-Nets in Base 4

(260−110, 260, 138)-Net over F₄ — Constructive and digital

Digital (150, 260, 138)-net over F₄, using

t-expansion [i] based on digital (149, 260, 138)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (21, 76, 34)-net over F₄, using
    - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
        T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
  2. digital (73, 184, 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]

(260−110, 260, 308)-Net over F₄ — Digital

Digital (150, 260, 308)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−110, 260, 4945)-Net in Base 4 — Upper bound on s

There is no (150, 260, 4946)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 460588 382906 927757 917391 236833 326274 075510 788995 370648 718866 041489 396630 890522 952680 954307 777566 973941 689699 455179 293708 127202 082036 653917 963953 861800 767648 > 4²⁶⁰ [i]