MinT - Best Known (181, 181+52, s)-Nets in Base 2

Best Known (181, 181+52, s)-Nets in Base 2

(181, 181+52, 260)-Net over F₂ — Constructive and digital

Digital (181, 233, 260)-net over F₂, using

2¹ times duplication [i] based on digital (180, 232, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 58, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(181, 181+52, 430)-Net over F₂ — Digital

Digital (181, 233, 430)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(181, 181+52, 5221)-Net in Base 2 — Upper bound on s

There is no (181, 233, 5222)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13829 551951 350508 587507 127077 590583 593769 783176 815855 940608 506961 844680 > 2²³³ [i]