MinT - Best Known (159, 159+73, s)-Nets in Base 4

Best Known (159, 159+73, s)-Nets in Base 4

(159, 159+73, 450)-Net over F₄ — Constructive and digital

Digital (159, 232, 450)-net over F₄, using

6 times m-reduction [i] based on digital (159, 238, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 119, 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]

(159, 159+73, 778)-Net over F₄ — Digital

Digital (159, 232, 778)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(159, 159+73, 34710)-Net in Base 4 — Upper bound on s

There is no (159, 232, 34711)-net in base 4, because

1 times m-reduction [i] would yield (159, 231, 34711)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 910336 343794 147083 826514 980078 476015 972665 883876 341980 244245 049745 403636 098198 891972 853281 457199 550902 846025 776560 691017 738273 534379 420036 > 4²³¹ [i]