MinT - Best Known (236−44, 236, s)-Nets in Base 2

Best Known (236−44, 236, s)-Nets in Base 2

(236−44, 236, 320)-Net over F₂ — Constructive and digital

Digital (192, 236, 320)-net over F₂, using

2¹ 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]

(236−44, 236, 745)-Net over F₂ — Digital

Digital (192, 236, 745)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−44, 236, 15316)-Net in Base 2 — Upper bound on s

There is no (192, 236, 15317)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 110480 850911 746333 704927 646886 363972 327304 291012 972422 183558 738693 701836 > 2²³⁶ [i]