MinT - Best Known (99−39, 99, s)-Nets in Base 2

Best Known (99−39, 99, s)-Nets in Base 2

(99−39, 99, 54)-Net over F₂ — Constructive and digital

Digital (60, 99, 54)-net over F₂, using

1 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]

(99−39, 99, 55)-Net over F₂ — Digital

Digital (60, 99, 55)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−39, 99, 256)-Net in Base 2 — Upper bound on s

There is no (60, 99, 257)-net in base 2, because

1 times m-reduction [i] would yield (60, 98, 257)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 332948 260899 078438 198235 117440 > 2⁹⁸ [i]