MinT - Best Known (250−47, 250, s)-Nets in Base 2

Best Known (250−47, 250, s)-Nets in Base 2

(250−47, 250, 320)-Net over F₂ — Constructive and digital

Digital (203, 250, 320)-net over F₂, using

trace code for nets [i] based on digital (3, 50, 64)-net over F₃₂, using
- net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(250−47, 250, 760)-Net over F₂ — Digital

Digital (203, 250, 760)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−47, 250, 17083)-Net in Base 2 — Upper bound on s

There is no (203, 250, 17084)-net in base 2, because

1 times m-reduction [i] would yield (203, 249, 17084)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 905 538878 097665 390826 138634 343408 006765 449722 900272 817634 256228 577485 617174 > 2²⁴⁹ [i]