MinT - Best Known (106−38, 106, s)-Nets in Base 2

Best Known (106−38, 106, s)-Nets in Base 2

(106−38, 106, 66)-Net over F₂ — Constructive and digital

Digital (68, 106, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 53, 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]

(106−38, 106, 71)-Net over F₂ — Digital

Digital (68, 106, 71)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−38, 106, 351)-Net in Base 2 — Upper bound on s

There is no (68, 106, 352)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 81 497073 562541 981188 126533 179159 > 2¹⁰⁶ [i]