MinT - Best Known (213−43, 213, s)-Nets in Base 2

Best Known (213−43, 213, s)-Nets in Base 2

(213−43, 213, 260)-Net over F₂ — Constructive and digital

Digital (170, 213, 260)-net over F₂, using

t-expansion [i] based on digital (168, 213, 260)-net over F₂, using
- 3 times m-reduction [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]

(213−43, 213, 532)-Net over F₂ — Digital

Digital (170, 213, 532)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−43, 213, 9463)-Net in Base 2 — Upper bound on s

There is no (170, 213, 9464)-net in base 2, because

1 times m-reduction [i] would yield (170, 212, 9464)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6591 832769 410925 054935 837212 406533 300281 467084 209020 839019 775585 > 2²¹² [i]