MinT - Best Known (119−49, 119, s)-Nets in Base 2

Best Known (119−49, 119, s)-Nets in Base 2

(119−49, 119, 54)-Net over F₂ — Constructive and digital

Digital (70, 119, 54)-net over F₂, using

1 times m-reduction [i] based on digital (70, 120, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 60, 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]

(119−49, 119, 57)-Net over F₂ — Digital

Digital (70, 119, 57)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−49, 119, 262)-Net in Base 2 — Upper bound on s

There is no (70, 119, 263)-net in base 2, because

1 times m-reduction [i] would yield (70, 118, 263)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 348573 500984 960136 120624 476374 230496 > 2¹¹⁸ [i]