MinT - Best Known (45, 45+43, s)-Nets in Base 8

Best Known (45, 45+43, s)-Nets in Base 8

(45, 45+43, 160)-Net over F₈ — Constructive and digital

Digital (45, 88, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 44, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(45, 45+43, 173)-Net over F₈ — Digital

Digital (45, 88, 173)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 45+43, 6822)-Net in Base 8 — Upper bound on s

There is no (45, 88, 6823)-net in base 8, because

1 times m-reduction [i] would yield (45, 87, 6823)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 711485 791571 286496 632469 630681 854270 630728 917072 074974 036520 240031 203968 307212 > 8⁸⁷ [i]