MinT - Best Known (235−77, 235, s)-Nets in Base 4

Best Known (235−77, 235, s)-Nets in Base 4

(235−77, 235, 450)-Net over F₄ — Constructive and digital

Digital (158, 235, 450)-net over F₄, using

1 times m-reduction [i] based on digital (158, 236, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 118, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(235−77, 235, 675)-Net over F₄ — Digital

Digital (158, 235, 675)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−77, 235, 25501)-Net in Base 4 — Upper bound on s

There is no (158, 235, 25502)-net in base 4, because

1 times m-reduction [i] would yield (158, 234, 25502)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 762 176629 111991 592940 634390 081073 479505 830481 075277 351508 452272 735508 971460 501384 404068 461689 699290 607251 419968 451552 060086 672991 011284 945392 > 4²³⁴ [i]