MinT - Best Known (55, 55+49, s)-Nets in Base 8

Best Known (55, 55+49, s)-Nets in Base 8

(55, 55+49, 208)-Net over F₈ — Constructive and digital

Digital (55, 104, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 52, 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]

(55, 55+49, 230)-Net over F₈ — Digital

Digital (55, 104, 230)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+49, 10505)-Net in Base 8 — Upper bound on s

There is no (55, 104, 10506)-net in base 8, because

1 times m-reduction [i] would yield (55, 103, 10506)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1044 572348 705575 839984 394491 048414 898389 992547 529720 556275 549813 484927 806735 286742 792493 022992 > 8¹⁰³ [i]