MinT - Best Known (243−72, 243, s)-Nets in Base 2

Best Known (243−72, 243, s)-Nets in Base 2

(243−72, 243, 135)-Net over F₂ — Constructive and digital

Digital (171, 243, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 81, 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]

(243−72, 243, 217)-Net over F₂ — Digital

Digital (171, 243, 217)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−72, 243, 1484)-Net in Base 2 — Upper bound on s

There is no (171, 243, 1485)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14 337274 715440 210743 218201 273331 535329 841086 022654 146861 352600 763487 905918 > 2²⁴³ [i]