MinT - Best Known (18, 18+19, s)-Nets in Base 8

Best Known (18, 18+19, s)-Nets in Base 8

(18, 18+19, 65)-Net over F₈ — Constructive and digital

Digital (18, 37, 65)-net over F₈, using

t-expansion [i] based on digital (14, 37, 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]

(18, 18+19, 77)-Net over F₈ — Digital

Digital (18, 37, 77)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(18, 18+19, 2421)-Net in Base 8 — Upper bound on s

There is no (18, 37, 2422)-net in base 8, because

1 times m-reduction [i] would yield (18, 36, 2422)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 325 238028 829579 186849 697892 430282 > 8³⁶ [i]