MinT - Best Known (150−40, 150, s)-Nets in Base 4

Best Known (150−40, 150, s)-Nets in Base 4

(150−40, 150, 531)-Net over F₄ — Constructive and digital

Digital (110, 150, 531)-net over F₄, using

t-expansion [i] based on digital (109, 150, 531)-net over F₄, using
- 3 times m-reduction [i] based on digital (109, 153, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 51, 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]

(150−40, 150, 1081)-Net over F₄ — Digital

Digital (110, 150, 1081)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−40, 150, 90689)-Net in Base 4 — Upper bound on s

There is no (110, 150, 90690)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 037213 957901 657995 440274 469417 456559 424513 868435 011468 544374 045074 933190 937052 226402 012976 > 4¹⁵⁰ [i]