MinT - Best Known (250−72, 250, s)-Nets in Base 2

Best Known (250−72, 250, s)-Nets in Base 2

(250−72, 250, 144)-Net over F₂ — Constructive and digital

Digital (178, 250, 144)-net over F₂, using

2¹ times duplication [i] based on digital (177, 249, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 83, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(250−72, 250, 238)-Net over F₂ — Digital

Digital (178, 250, 238)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−72, 250, 1706)-Net in Base 2 — Upper bound on s

There is no (178, 250, 1707)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1844 372993 145627 500015 095468 346817 766512 591187 801470 927526 363868 764723 995610 > 2²⁵⁰ [i]