MinT - Best Known (105−49, 105, s)-Nets in Base 8

Best Known (105−49, 105, s)-Nets in Base 8

(105−49, 105, 208)-Net over F₈ — Constructive and digital

Digital (56, 105, 208)-net over F₈, using

1 times m-reduction [i] based on digital (56, 106, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 53, 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]

(105−49, 105, 241)-Net over F₈ — Digital

Digital (56, 105, 241)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−49, 105, 11457)-Net in Base 8 — Upper bound on s

There is no (56, 105, 11458)-net in base 8, because

1 times m-reduction [i] would yield (56, 104, 11458)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8352 659579 116215 292011 669889 564548 695869 758661 800058 685615 724607 588781 416550 478338 888826 169688 > 8¹⁰⁴ [i]