MinT - Best Known (161, 161+36, s)-Nets in Base 2

Best Known (161, 161+36, s)-Nets in Base 2

(161, 161+36, 320)-Net over F₂ — Constructive and digital

Digital (161, 197, 320)-net over F₂, using

2² times duplication [i] based on digital (159, 195, 320)-net over F₂, using
- trace code for nets [i] based on digital (3, 39, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(161, 161+36, 692)-Net over F₂ — Digital

Digital (161, 197, 692)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(161, 161+36, 14858)-Net in Base 2 — Upper bound on s

There is no (161, 197, 14859)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 201089 506329 279304 078006 862157 050556 718941 290147 061803 790880 > 2¹⁹⁷ [i]