MinT - Best Known (120−49, 120, s)-Nets in Base 2

Best Known (120−49, 120, s)-Nets in Base 2

(120−49, 120, 54)-Net over F₂ — Constructive and digital

Digital (71, 120, 54)-net over F₂, using

2 times m-reduction [i] based on digital (71, 122, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 61, 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]

(120−49, 120, 58)-Net over F₂ — Digital

Digital (71, 120, 58)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−49, 120, 271)-Net in Base 2 — Upper bound on s

There is no (71, 120, 272)-net in base 2, because

1 times m-reduction [i] would yield (71, 119, 272)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 716980 807301 397565 644702 397802 288368 > 2¹¹⁹ [i]