MinT - Best Known (38, 38+32, s)-Nets in Base 2

Best Known (38, 38+32, s)-Nets in Base 2

(38, 38+32, 28)-Net over F₂ — Constructive and digital

Digital (38, 70, 28)-net over F₂, using

trace code for nets [i] based on digital (3, 35, 14)-net over F₄, using
- net from sequence [i] based on digital (3, 13)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
    - an explicitly constructive algebraic function field [i]

(38, 38+32, 31)-Net over F₂ — Digital

Digital (38, 70, 31)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+32, 107)-Net in Base 2 — Upper bound on s

There is no (38, 70, 108)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2⁷⁰, 108, S₂, 32), but
- the linear programming bound shows that MÂ â‰¥ 4 297708 243581 570312 211812 843520 / 3462 071301 > 2⁷⁰ [i]