MinT - Best Known (115−53, 115, s)-Nets in Base 8

Best Known (115−53, 115, s)-Nets in Base 8

(115−53, 115, 208)-Net over F₈ — Constructive and digital

Digital (62, 115, 208)-net over F₈, using

3 times m-reduction [i] based on digital (62, 118, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 59, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(115−53, 115, 273)-Net over F₈ — Digital

Digital (62, 115, 273)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−53, 115, 13720)-Net in Base 8 — Upper bound on s

There is no (62, 115, 13721)-net in base 8, because

1 times m-reduction [i] would yield (62, 114, 13721)-net in base 8, but
- 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]