MinT - Best Known (38, 38+38, s)-Nets in Base 8

Best Known (38, 38+38, s)-Nets in Base 8

(38, 38+38, 130)-Net over F₈ — Constructive and digital

Digital (38, 76, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 38, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(38, 38+38, 141)-Net over F₈ — Digital

Digital (38, 76, 141)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+38, 4627)-Net in Base 8 — Upper bound on s

There is no (38, 76, 4628)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 431 603756 836859 207785 988256 710573 631837 252627 962073 778183 202150 800383 > 8⁷⁶ [i]