MinT - Best Known (168, 168+70, s)-Nets in Base 2

Best Known (168, 168+70, s)-Nets in Base 2

(168, 168+70, 135)-Net over F₂ — Constructive and digital

Digital (168, 238, 135)-net over F₂, using

2¹ times duplication [i] based on digital (167, 237, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 79, 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]

(168, 168+70, 217)-Net over F₂ — Digital

Digital (168, 238, 217)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(168, 168+70, 1498)-Net in Base 2 — Upper bound on s

There is no (168, 238, 1499)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 446157 005815 221343 700772 024031 221545 805241 311237 095942 875081 515346 635876 > 2²³⁸ [i]