MinT - Best Known (232−52, 232, s)-Nets in Base 2

Best Known (232−52, 232, s)-Nets in Base 2

(232−52, 232, 260)-Net over F₂ — Constructive and digital

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]

(232−52, 232, 423)-Net over F₂ — Digital

Digital (180, 232, 423)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−52, 232, 5083)-Net in Base 2 — Upper bound on s

There is no (180, 232, 5084)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6928 218796 284204 892879 033355 601691 700131 417550 355153 863447 341235 831375 > 2²³² [i]