MinT - Best Known (254−75, 254, s)-Nets in Base 2

Best Known (254−75, 254, s)-Nets in Base 2

(254−75, 254, 135)-Net over F₂ — Constructive and digital

Digital (179, 254, 135)-net over F₂, using

1 times m-reduction [i] based on digital (179, 255, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 85, 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]

(254−75, 254, 227)-Net over F₂ — Digital

Digital (179, 254, 227)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(254−75, 254, 1621)-Net in Base 2 — Upper bound on s

There is no (179, 254, 1622)-net in base 2, because

1 times m-reduction [i] would yield (179, 253, 1622)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14494 331668 929382 179022 890600 068073 639316 333879 867077 238675 148910 576821 577438 > 2²⁵³ [i]