MinT - Best Known (42, 42+40, s)-Nets in Base 8

Best Known (42, 42+40, s)-Nets in Base 8

(42, 42+40, 160)-Net over F₈ — Constructive and digital

Digital (42, 82, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 41, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(42, 42+40, 165)-Net over F₈ — Digital

Digital (42, 82, 165)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+40, 5970)-Net in Base 8 — Upper bound on s

There is no (42, 82, 5971)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 113 428753 898064 645620 544001 343831 378360 459004 880666 716359 240127 586277 429776 > 8⁸² [i]