MinT - Best Known (122−57, 122, s)-Nets in Base 8

Best Known (122−57, 122, s)-Nets in Base 8

(122−57, 122, 208)-Net over F₈ — Constructive and digital

Digital (65, 122, 208)-net over F₈, using

2 times m-reduction [i] based on digital (65, 124, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 62, 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]

(122−57, 122, 272)-Net over F₈ — Digital

Digital (65, 122, 272)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−57, 122, 12881)-Net in Base 8 — Upper bound on s

There is no (65, 122, 12882)-net in base 8, because

1 times m-reduction [i] would yield (65, 121, 12882)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 18 820794 796043 107383 766436 892187 738498 448837 694466 522656 623776 032795 145120 039853 382227 008805 896766 889387 671408 > 8¹²¹ [i]