MinT - Best Known (212, 212+48, s)-Nets in Base 2

Best Known (212, 212+48, s)-Nets in Base 2

(212, 212+48, 320)-Net over F₂ — Constructive and digital

Digital (212, 260, 320)-net over F₂, using

t-expansion [i] based on digital (211, 260, 320)-net over F₂, using
- trace code for nets [i] based on digital (3, 52, 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]

(212, 212+48, 833)-Net over F₂ — Digital

Digital (212, 260, 833)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(212, 212+48, 17850)-Net in Base 2 — Upper bound on s

There is no (212, 260, 17851)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 853038 285575 857312 785537 142373 564254 784851 556432 624999 957169 855834 607491 014431 > 2²⁶⁰ [i]