MinT - Best Known (141, 236, s)-Nets in Base 4

Best Known (141, 236, s)-Nets in Base 4

(141, 236, 138)-Net over F₄ — Constructive and digital

Digital (141, 236, 138)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (21, 68, 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, 168, 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]

(141, 236, 332)-Net over F₄ — Digital

Digital (141, 236, 332)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 236, 6231)-Net in Base 4 — Upper bound on s

There is no (141, 236, 6232)-net in base 4, because

1 times m-reduction [i] would yield (141, 235, 6232)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3058 298462 127153 464658 589756 492325 532703 891972 475982 642221 656069 210762 394254 102221 437798 338169 074898 891232 231775 768129 846958 355803 788073 202100 > 4²³⁵ [i]