MinT - Best Known (10, 10+40, s)-Nets in Base 27

Best Known (10, 10+40, s)-Nets in Base 27

(10, 10+40, 94)-Net over F₂₇ — Constructive and digital

Digital (10, 50, 94)-net over F₂₇, using

net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
  - a function field by SÃ©mirat [i]

(10, 10+40, 99)-Net over F₂₇ — Digital

Digital (10, 50, 99)-net over F₂₇, using

t-expansion [i] based on digital (9, 50, 99)-net over F₂₇, using
- net from sequence [i] based on digital (9, 98)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 99, using
    - a curve from the manYPoints database [i]

(10, 10+40, 1199)-Net in Base 27 — Upper bound on s

There is no (10, 50, 1200)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 372253 538318 472901 419727 101411 688472 285119 790909 147340 318169 484848 760961 > 27⁵⁰ [i]