MinT - Best Known (146, 146+56, s)-Nets in Base 2

Best Known (146, 146+56, s)-Nets in Base 2

(146, 146+56, 144)-Net over F₂ — Constructive and digital

Digital (146, 202, 144)-net over F₂, using

2¹ times duplication [i] based on digital (145, 201, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 67, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(146, 146+56, 217)-Net over F₂ — Digital

Digital (146, 202, 217)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 146+56, 1636)-Net in Base 2 — Upper bound on s

There is no (146, 202, 1637)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 461018 068064 065281 092222 985696 908409 052053 720197 263807 096620 > 2²⁰² [i]