MinT - Best Known (161−34, 161, s)-Nets in Base 2

Best Known (161−34, 161, s)-Nets in Base 2

(161−34, 161, 260)-Net over F₂ — Constructive and digital

Digital (127, 161, 260)-net over F₂, using

2¹ times duplication [i] based on digital (126, 160, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 40, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(161−34, 161, 371)-Net over F₂ — Digital

Digital (127, 161, 371)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(161−34, 161, 5066)-Net in Base 2 — Upper bound on s

There is no (127, 161, 5067)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 923839 693206 080389 485714 120111 287416 634614 375504 > 2¹⁶¹ [i]