MinT - Best Known (255−76, 255, s)-Nets in Base 2

Best Known (255−76, 255, s)-Nets in Base 2

(255−76, 255, 135)-Net over F₂ — Constructive and digital

Digital (179, 255, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 85, 45)-net over F₈, using
- net from sequence [i] based on digital (9, 44)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
    - an explicitly constructive algebraic function field [i]

(255−76, 255, 223)-Net over F₂ — Digital

Digital (179, 255, 223)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(255−76, 255, 1517)-Net in Base 2 — Upper bound on s

There is no (179, 255, 1518)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 57988 115060 198432 975327 734522 360936 838850 907720 528947 306572 352151 196139 623684 > 2²⁵⁵ [i]