MinT - Best Known (154−62, 154, s)-Nets in Base 2

Best Known (154−62, 154, s)-Nets in Base 2

(154−62, 154, 66)-Net over F₂ — Constructive and digital

Digital (92, 154, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 77, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(154−62, 154, 73)-Net over F₂ — Digital

Digital (92, 154, 73)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−62, 154, 344)-Net in Base 2 — Upper bound on s

There is no (92, 154, 345)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 23003 109261 687999 077018 110453 499568 056282 308480 > 2¹⁵⁴ [i]