MinT - Best Known (228−50, 228, s)-Nets in Base 2

Best Known (228−50, 228, s)-Nets in Base 2

(228−50, 228, 260)-Net over F₂ — Constructive and digital

Digital (178, 228, 260)-net over F₂, using

t-expansion [i] based on digital (177, 228, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 57, 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]

(228−50, 228, 442)-Net over F₂ — Digital

Digital (178, 228, 442)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−50, 228, 5625)-Net in Base 2 — Upper bound on s

There is no (178, 228, 5626)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 431 824460 383908 424816 032226 694375 074337 698303 277416 215799 856718 207157 > 2²²⁸ [i]