MinT - Best Known (94−22, 94, s)-Nets in Base 2

Best Known (94−22, 94, s)-Nets in Base 2

(94−22, 94, 135)-Net over F₂ — Constructive and digital

Digital (72, 94, 135)-net over F₂, using

2¹ times duplication [i] based on digital (71, 93, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 31, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(94−22, 94, 186)-Net over F₂ — Digital

Digital (72, 94, 186)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(94−22, 94, 1818)-Net in Base 2 — Upper bound on s

There is no (72, 94, 1819)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 19892 008308 045755 427966 259050 > 2⁹⁴ [i]