MinT - Best Known (218−48, 218, s)-Nets in Base 2

Best Known (218−48, 218, s)-Nets in Base 2

(218−48, 218, 260)-Net over F₂ — Constructive and digital

Digital (170, 218, 260)-net over F₂, using

2² times duplication [i] based on digital (168, 216, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 54, 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]

(218−48, 218, 421)-Net over F₂ — Digital

Digital (170, 218, 421)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−48, 218, 5282)-Net in Base 2 — Upper bound on s

There is no (170, 218, 5283)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 422690 857433 565633 689602 585721 110391 738122 610304 828059 117603 555612 > 2²¹⁸ [i]