MinT - Best Known (58, 58+56, s)-Nets in Base 8

Best Known (58, 58+56, s)-Nets in Base 8

(58, 58+56, 160)-Net over F₈ — Constructive and digital

Digital (58, 114, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 57, 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]

(58, 58+56, 209)-Net over F₈ — Digital

Digital (58, 114, 209)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+56, 7652)-Net in Base 8 — Upper bound on s

There is no (58, 114, 7653)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8 987682 006155 015498 301703 265657 195677 338030 262913 594737 420677 728421 845146 073837 430541 151823 407696 184060 > 8¹¹⁴ [i]