MinT - Best Known (230−43, 230, s)-Nets in Base 2

Best Known (230−43, 230, s)-Nets in Base 2

(230−43, 230, 320)-Net over F₂ — Constructive and digital

Digital (187, 230, 320)-net over F₂, using

trace code for nets [i] based on digital (3, 46, 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]

(230−43, 230, 723)-Net over F₂ — Digital

Digital (187, 230, 723)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−43, 230, 16609)-Net in Base 2 — Upper bound on s

There is no (187, 230, 16610)-net in base 2, because

1 times m-reduction [i] would yield (187, 229, 16610)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 863 792642 613638 302965 940104 786235 205375 423334 178532 693951 244333 416328 > 2²²⁹ [i]