MinT - Best Known (114−53, 114, s)-Nets in Base 4

Best Known (114−53, 114, s)-Nets in Base 4

(114−53, 114, 90)-Net over F₄ — Constructive and digital

Digital (61, 114, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 57, 45)-net over F₁₆, using
- net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
    - a function field by GarcÃa and Quoos [i]

(114−53, 114, 112)-Net over F₄ — Digital

Digital (61, 114, 112)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(114−53, 114, 1433)-Net in Base 4 — Upper bound on s

There is no (61, 114, 1434)-net in base 4, because

1 times m-reduction [i] would yield (61, 113, 1434)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 108 230933 342600 914961 866824 725465 356471 993865 926045 353160 973322 657160 > 4¹¹³ [i]