MinT - Best Known (142, 236, s)-Nets in Base 4

Best Known (142, 236, s)-Nets in Base 4

(142, 236, 138)-Net over F₄ — Constructive and digital

Digital (142, 236, 138)-net over F₄, using

2 times m-reduction [i] based on digital (142, 238, 138)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (21, 69, 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, 169, 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]

(142, 236, 343)-Net over F₄ — Digital

Digital (142, 236, 343)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 236, 6419)-Net in Base 4 — Upper bound on s

There is no (142, 236, 6420)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12259 341700 379900 325119 163152 228241 083697 634405 540664 262863 739975 546021 143747 471428 802497 129862 725591 593484 207726 576649 206250 484268 925890 534048 > 4²³⁶ [i]