MinT - Best Known (60, 60+38, s)-Nets in Base 2

Best Known (60, 60+38, s)-Nets in Base 2

(60, 60+38, 54)-Net over F₂ — Constructive and digital

Digital (60, 98, 54)-net over F₂, using

2 times m-reduction [i] based on digital (60, 100, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 50, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]

(60, 60+38, 56)-Net over F₂ — Digital

Digital (60, 98, 56)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+38, 256)-Net in Base 2 — Upper bound on s

There is no (60, 98, 257)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 332948 260899 078438 198235 117440 > 2⁹⁸ [i]