MinT - Best Known (51−27, 51, s)-Nets in Base 8

Best Known (51−27, 51, s)-Nets in Base 8

(51−27, 51, 65)-Net over F₈ — Constructive and digital

Digital (24, 51, 65)-net over F₈, using

t-expansion [i] based on digital (14, 51, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(51−27, 51, 84)-Net over F₈ — Digital

Digital (24, 51, 84)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(51−27, 51, 2400)-Net in Base 8 — Upper bound on s

There is no (24, 51, 2401)-net in base 8, because

1 times m-reduction [i] would yield (24, 50, 2401)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1430 601284 705790 503635 828032 748442 258160 469088 > 8⁵⁰ [i]