MinT - Best Known (66, 66+55, s)-Nets in Base 4

Best Known (66, 66+55, s)-Nets in Base 4

(66, 66+55, 98)-Net over F₄ — Constructive and digital

Digital (66, 121, 98)-net over F₄, using

1 times m-reduction [i] based on digital (66, 122, 98)-net over F₄, using
- trace code for nets [i] based on digital (5, 61, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(66, 66+55, 127)-Net over F₄ — Digital

Digital (66, 121, 127)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+55, 1704)-Net in Base 4 — Upper bound on s

There is no (66, 121, 1705)-net in base 4, because

1 times m-reduction [i] would yield (66, 120, 1705)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 784252 976210 573384 790338 552865 623216 832876 132896 485331 442534 744770 143968 > 4¹²⁰ [i]