MinT - Best Known (136, 240, s)-Nets in Base 4

Best Known (136, 240, s)-Nets in Base 4

(136, 240, 131)-Net over F₄ — Constructive and digital

Digital (136, 240, 131)-net over F₄, using

2 times m-reduction [i] based on digital (136, 242, 131)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 63, 27)-net over F₄, using
    - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
        an explicitly constructive algebraic function field [i]
  2. digital (73, 179, 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]

(136, 240, 265)-Net over F₄ — Digital

Digital (136, 240, 265)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 240, 4007)-Net in Base 4 — Upper bound on s

There is no (136, 240, 4008)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 126106 185070 566822 179863 602967 291302 067139 287534 477403 463105 776134 371177 036161 283765 549465 434702 372981 167479 665808 750784 753685 265031 776485 723368 > 4²⁴⁰ [i]