MinT - Best Known (36, 64, s)-Nets in Base 2

Best Known (36, 64, s)-Nets in Base 2

(36, 64, 30)-Net over F₂ — Constructive and digital

Digital (36, 64, 30)-net over F₂, using

trace code for nets [i] based on digital (4, 32, 15)-net over F₄, using
- net from sequence [i] based on digital (4, 14)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
    - an explicitly constructive algebraic function field [i]

(36, 64, 32)-Net over F₂ — Digital

Digital (36, 64, 32)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(36, 64, 124)-Net in Base 2 — Upper bound on s

There is no (36, 64, 125)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 19 421206 003812 714876 > 2⁶⁴ [i]