MinT - Best Known (198−55, 198, s)-Nets in Base 2

Best Known (198−55, 198, s)-Nets in Base 2

(198−55, 198, 144)-Net over F₂ — Constructive and digital

Digital (143, 198, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 66, 48)-net over F₈, using
- net from sequence [i] based on digital (11, 47)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
    - a function field by SÃ©mirat [i]

(198−55, 198, 213)-Net over F₂ — Digital

Digital (143, 198, 213)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−55, 198, 1677)-Net in Base 2 — Upper bound on s

There is no (143, 198, 1678)-net in base 2, because

1 times m-reduction [i] would yield (143, 197, 1678)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 202195 593396 174372 978256 476343 539423 044361 559528 135638 936112 > 2¹⁹⁷ [i]