MinT - Best Known (102, 102+39, s)-Nets in Base 4

Best Known (102, 102+39, s)-Nets in Base 4

(102, 102+39, 531)-Net over F₄ — Constructive and digital

Digital (102, 141, 531)-net over F₄, using

t-expansion [i] based on digital (101, 141, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 47, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(102, 102+39, 877)-Net over F₄ — Digital

Digital (102, 141, 877)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+39, 72149)-Net in Base 4 — Upper bound on s

There is no (102, 141, 72150)-net in base 4, because

1 times m-reduction [i] would yield (102, 140, 72150)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 942910 932020 575207 383824 575174 418127 168599 375246 568366 462276 101225 528910 111989 197446 > 4¹⁴⁰ [i]