MinT - Best Known (38, 38+40, s)-Nets in Base 128

Best Known (38, 38+40, s)-Nets in Base 128

(38, 38+40, 576)-Net over F₁₂₈ — Constructive and digital

Digital (38, 78, 576)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 29, 288)-net over F₁₂₈, using
  - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
      - a function field by SÃ©mirat [i]
2. digital (9, 49, 288)-net over F₁₂₈, using
  - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈ (see above)

(38, 38+40, 2006)-Net over F₁₂₈ — Digital

Digital (38, 78, 2006)-net over F₁₂₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+40, large)-Net in Base 128 — Upper bound on s

There is no (38, 78, large)-net in base 128, because

38 times m-reduction [i] would yield (38, 40, large)-net in base 128, but
- mutually orthogonal hypercube bound [i]