MinT - Best Known (259−44, 259, s)-Nets in Base 2

Best Known (259−44, 259, s)-Nets in Base 2

(259−44, 259, 490)-Net over F₂ — Constructive and digital

Digital (215, 259, 490)-net over F₂, using

1 times m-reduction [i] based on digital (215, 260, 490)-net over F₂, using
- trace code for nets [i] based on digital (7, 52, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(259−44, 259, 1111)-Net over F₂ — Digital

Digital (215, 259, 1111)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−44, 259, 31648)-Net in Base 2 — Upper bound on s

There is no (215, 259, 31649)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 926733 803261 124516 458337 378388 845485 948530 849064 425652 369719 718181 441955 559184 > 2²⁵⁹ [i]