MinT - Best Known (156−68, 156, s)-Nets in Base 2

Best Known (156−68, 156, s)-Nets in Base 2

(156−68, 156, 54)-Net over F₂ — Constructive and digital

Digital (88, 156, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 78, 27)-net over F₄, using
- net from sequence [i] based on digital (10, 26)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]

(156−68, 156, 62)-Net over F₂ — Digital

Digital (88, 156, 62)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−68, 156, 278)-Net in Base 2 — Upper bound on s

There is no (88, 156, 279)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 97396 964141 390474 255218 783200 426578 886923 593272 > 2¹⁵⁶ [i]