MinT - Best Known (256−74, 256, s)-Nets in Base 2

Best Known (256−74, 256, s)-Nets in Base 2

(256−74, 256, 144)-Net over F₂ — Constructive and digital

Digital (182, 256, 144)-net over F₂, using

2¹ times duplication [i] based on digital (181, 255, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 85, 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]

(256−74, 256, 241)-Net over F₂ — Digital

Digital (182, 256, 241)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−74, 256, 1718)-Net in Base 2 — Upper bound on s

There is no (182, 256, 1719)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 116300 158216 174731 876589 359175 207281 963392 052022 628121 046853 891919 660101 534340 > 2²⁵⁶ [i]