MinT - Best Known (202−42, 202, s)-Nets in Base 2

Best Known (202−42, 202, s)-Nets in Base 2

(202−42, 202, 260)-Net over F₂ — Constructive and digital

Digital (160, 202, 260)-net over F₂, using

t-expansion [i] based on digital (159, 202, 260)-net over F₂, using
- 2 times m-reduction [i] based on digital (159, 204, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 51, 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]

(202−42, 202, 466)-Net over F₂ — Digital

Digital (160, 202, 466)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−42, 202, 6794)-Net in Base 2 — Upper bound on s

There is no (160, 202, 6795)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 442619 461022 604702 476051 668791 207088 311547 494485 947424 909312 > 2²⁰² [i]