MinT - Best Known (6, 41, s)-Nets in Base 27

Best Known (6, 41, s)-Nets in Base 27

(6, 41, 76)-Net over F₂₇ — Constructive and digital

Digital (6, 41, 76)-net over F₂₇, using

net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
  - a function field by SÃ©mirat [i]

(6, 41, 635)-Net in Base 27 — Upper bound on s

There is no (6, 41, 636)-net in base 27, because

1 times m-reduction [i] would yield (6, 40, 636)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1826 927511 842130 648525 623859 415991 310022 342400 150144 400537 > 27⁴⁰ [i]