MinT - Best Known (213−62, 213, s)-Nets in Base 2

Best Known (213−62, 213, s)-Nets in Base 2

(213−62, 213, 135)-Net over F₂ — Constructive and digital

Digital (151, 213, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 71, 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]

(213−62, 213, 203)-Net over F₂ — Digital

Digital (151, 213, 203)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−62, 213, 1408)-Net in Base 2 — Upper bound on s

There is no (151, 213, 1409)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13417 529539 961238 014450 555140 125833 995302 828406 644714 838339 338240 > 2²¹³ [i]