MinT - Best Known (122−51, 122, s)-Nets in Base 2

Best Known (122−51, 122, s)-Nets in Base 2

(122−51, 122, 54)-Net over F₂ — Constructive and digital

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]

(122−51, 122, 56)-Net over F₂ — Digital

Digital (71, 122, 56)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−51, 122, 256)-Net in Base 2 — Upper bound on s

There is no (71, 122, 257)-net in base 2, because

1 times m-reduction [i] would yield (71, 121, 257)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 779309 522364 477995 861362 319446 929472 > 2¹²¹ [i]