MinT - Best Known (218−46, 218, s)-Nets in Base 2

Best Known (218−46, 218, s)-Nets in Base 2

(218−46, 218, 260)-Net over F₂ — Constructive and digital

Digital (172, 218, 260)-net over F₂, using

t-expansion [i] based on digital (171, 218, 260)-net over F₂, using
- 2 times m-reduction [i] based on digital (171, 220, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 55, 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]

(218−46, 218, 475)-Net over F₂ — Digital

Digital (172, 218, 475)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−46, 218, 6691)-Net in Base 2 — Upper bound on s

There is no (172, 218, 6692)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 422471 272573 730924 873623 645218 851004 722676 746104 255214 592556 099080 > 2²¹⁸ [i]