MinT - Best Known (141, 141+107, s)-Nets in Base 4

Best Known (141, 141+107, s)-Nets in Base 4

(141, 141+107, 137)-Net over F₄ — Constructive and digital

Digital (141, 248, 137)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (15, 68, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
2. digital (73, 180, 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, 141+107, 277)-Net over F₄ — Digital

Digital (141, 248, 277)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 141+107, 4346)-Net in Base 4 — Upper bound on s

There is no (141, 248, 4347)-net in base 4, because

1 times m-reduction [i] would yield (141, 247, 4347)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51256 705088 179356 505955 254073 744981 738177 678331 265188 004351 187897 932035 776618 167755 326660 622518 234750 238216 726724 293100 725054 498867 147790 013695 949020 > 4²⁴⁷ [i]