MinT - Best Known (73, 73+49, s)-Nets in Base 2

Best Known (73, 73+49, s)-Nets in Base 2

(73, 73+49, 56)-Net over F₂ — Constructive and digital

Digital (73, 122, 56)-net over F₂, using

trace code for nets [i] based on digital (12, 61, 28)-net over F₄, using
- net from sequence [i] based on digital (12, 27)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(73, 73+49, 61)-Net over F₂ — Digital

Digital (73, 122, 61)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+49, 289)-Net in Base 2 — Upper bound on s

There is no (73, 122, 290)-net in base 2, because

1 times m-reduction [i] would yield (73, 121, 290)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 849561 430076 072954 679695 626228 855004 > 2¹²¹ [i]