MinT - Best Known (116−53, 116, s)-Nets in Base 4

Best Known (116−53, 116, s)-Nets in Base 4

(116−53, 116, 98)-Net over F₄ — Constructive and digital

Digital (63, 116, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 58, 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]

(116−53, 116, 121)-Net over F₄ — Digital

Digital (63, 116, 121)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−53, 116, 1597)-Net in Base 4 — Upper bound on s

There is no (63, 116, 1598)-net in base 4, because

1 times m-reduction [i] would yield (63, 115, 1598)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1739 305009 069969 718262 281951 691355 333126 306827 376365 367846 498229 942410 > 4¹¹⁵ [i]