MinT - Best Known (237−72, 237, s)-Nets in Base 4

Best Known (237−72, 237, s)-Nets in Base 4

(237−72, 237, 531)-Net over F₄ — Constructive and digital

Digital (165, 237, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 79, 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]

(237−72, 237, 911)-Net over F₄ — Digital

Digital (165, 237, 911)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−72, 237, 43740)-Net in Base 4 — Upper bound on s

There is no (165, 237, 43741)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48793 455225 811716 067250 063454 625363 680489 843214 764457 159863 932764 133831 294448 733152 418248 903211 276449 909961 733994 889036 479697 286606 502534 445450 > 4²³⁷ [i]