MinT - Best Known (159−39, 159, s)-Nets in Base 2

Best Known (159−39, 159, s)-Nets in Base 2

(159−39, 159, 195)-Net over F₂ — Constructive and digital

Digital (120, 159, 195)-net over F₂, using

trace code for nets [i] based on digital (14, 53, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(159−39, 159, 244)-Net over F₂ — Digital

Digital (120, 159, 244)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−39, 159, 2498)-Net in Base 2 — Upper bound on s

There is no (120, 159, 2499)-net in base 2, because

1 times m-reduction [i] would yield (120, 158, 2499)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 366392 492166 917574 617974 994750 496919 035148 510232 > 2¹⁵⁸ [i]