MinT - Best Known (202−77, 202, s)-Nets in Base 4

Best Known (202−77, 202, s)-Nets in Base 4

(202−77, 202, 134)-Net over F₄ — Constructive and digital

Digital (125, 202, 134)-net over F₄, using

1 times m-reduction [i] based on digital (125, 203, 134)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 52, 30)-net over F₄, using
    - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
        F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
  2. digital (73, 151, 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]

(202−77, 202, 347)-Net over F₄ — Digital

Digital (125, 202, 347)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−77, 202, 7629)-Net in Base 4 — Upper bound on s

There is no (125, 202, 7630)-net in base 4, because

1 times m-reduction [i] would yield (125, 201, 7630)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 355934 021495 264713 799238 788119 276815 032780 737357 817001 204849 787650 476433 580884 594065 680554 253784 555742 665511 885132 327384 > 4²⁰¹ [i]