MinT - Best Known (114−31, 114, s)-Nets in Base 2

Best Known (114−31, 114, s)-Nets in Base 2

(114−31, 114, 102)-Net over F₂ — Constructive and digital

Digital (83, 114, 102)-net over F₂, using

trace code for nets [i] based on digital (7, 38, 34)-net over F₈, using
- net from sequence [i] based on digital (7, 33)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
    - a function field by SÃ©mirat [i]

(114−31, 114, 146)-Net over F₂ — Digital

Digital (83, 114, 146)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(114−31, 114, 1168)-Net in Base 2 — Upper bound on s

There is no (83, 114, 1169)-net in base 2, because

1 times m-reduction [i] would yield (83, 113, 1169)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10499 766419 873003 332849 834527 561728 > 2¹¹³ [i]