MinT - Best Known (117, 117+31, s)-Nets in Base 2

Best Known (117, 117+31, s)-Nets in Base 2

(117, 117+31, 260)-Net over F₂ — Constructive and digital

Digital (117, 148, 260)-net over F₂, using

trace code for nets [i] based on digital (6, 37, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(117, 117+31, 357)-Net over F₂ — Digital

Digital (117, 148, 357)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+31, 5704)-Net in Base 2 — Upper bound on s

There is no (117, 148, 5705)-net in base 2, because

1 times m-reduction [i] would yield (117, 147, 5705)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 178 798827 152675 857740 209873 260713 283425 995648 > 2¹⁴⁷ [i]