MinT - Best Known (120−45, 120, s)-Nets in Base 2

Best Known (120−45, 120, s)-Nets in Base 2

(120−45, 120, 66)-Net over F₂ — Constructive and digital

Digital (75, 120, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 60, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(120−45, 120, 71)-Net over F₂ — Digital

Digital (75, 120, 71)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(120−45, 120, 353)-Net in Base 2 — Upper bound on s

There is no (75, 120, 354)-net in base 2, because

1 times m-reduction [i] would yield (75, 119, 354)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 687016 428907 962980 852649 170021 990384 > 2¹¹⁹ [i]