MinT - Best Known (166−46, 166, s)-Nets in Base 2

Best Known (166−46, 166, s)-Nets in Base 2

(166−46, 166, 135)-Net over F₂ — Constructive and digital

Digital (120, 166, 135)-net over F₂, using

2¹ times duplication [i] based on digital (119, 165, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 55, 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]

(166−46, 166, 185)-Net over F₂ — Digital

Digital (120, 166, 185)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−46, 166, 1369)-Net in Base 2 — Upper bound on s

There is no (120, 166, 1370)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 94 256201 179817 551139 068067 433993 009372 718107 803932 > 2¹⁶⁶ [i]