MinT - Best Known (178−74, 178, s)-Nets in Base 2

Best Known (178−74, 178, s)-Nets in Base 2

(178−74, 178, 66)-Net over F₂ — Constructive and digital

Digital (104, 178, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 89, 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]

(178−74, 178, 77)-Net over F₂ — Digital

Digital (104, 178, 77)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−74, 178, 359)-Net in Base 2 — Upper bound on s

There is no (104, 178, 360)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 404944 552818 026750 305302 453909 388596 033412 310315 359053 > 2¹⁷⁸ [i]