MinT - Best Known (116−49, 116, s)-Nets in Base 2

Best Known (116−49, 116, s)-Nets in Base 2

(116−49, 116, 44)-Net over F₂ — Constructive and digital

Digital (67, 116, 44)-net over F₂, using

trace code for nets [i] based on digital (9, 58, 22)-net over F₄, using
- net from sequence [i] based on digital (9, 21)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 22, using
    - an explicitly constructive algebraic function field [i]

(116−49, 116, 53)-Net over F₂ — Digital

Digital (67, 116, 53)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−49, 116, 237)-Net in Base 2 — Upper bound on s

There is no (67, 116, 238)-net in base 2, because

1 times m-reduction [i] would yield (67, 115, 238)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 41565 424801 630098 015665 632657 369226 > 2¹¹⁵ [i]