MinT - Best Known (237−44, 237, s)-Nets in Base 2

Best Known (237−44, 237, s)-Nets in Base 2

(237−44, 237, 320)-Net over F₂ — Constructive and digital

Digital (193, 237, 320)-net over F₂, using

2² times duplication [i] based on digital (191, 235, 320)-net over F₂, using
- trace code for nets [i] based on digital (3, 47, 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]

(237−44, 237, 758)-Net over F₂ — Digital

Digital (193, 237, 758)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−44, 237, 15807)-Net in Base 2 — Upper bound on s

There is no (193, 237, 15808)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 220866 861402 213674 192324 602903 191922 567185 103772 405267 678307 299430 657309 > 2²³⁷ [i]