MinT - Best Known (62, 62+52, s)-Nets in Base 8

Best Known (62, 62+52, s)-Nets in Base 8

(62, 62+52, 256)-Net over F₈ — Constructive and digital

Digital (62, 114, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 57, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(62, 62+52, 283)-Net over F₈ — Digital

Digital (62, 114, 283)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+52, 13720)-Net in Base 8 — Upper bound on s

There is no (62, 114, 13721)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8 959641 889349 720956 275518 203360 657717 120104 429724 113319 127319 630477 258929 371192 885075 774519 501251 632512 > 8¹¹⁴ [i]