MinT - Best Known (102−36, 102, s)-Nets in Base 2

Best Known (102−36, 102, s)-Nets in Base 2

(102−36, 102, 66)-Net over F₂ — Constructive and digital

Digital (66, 102, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 51, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(102−36, 102, 72)-Net over F₂ — Digital

Digital (66, 102, 72)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−36, 102, 357)-Net in Base 2 — Upper bound on s

There is no (66, 102, 358)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 075555 852477 127916 947945 630340 > 2¹⁰² [i]