MinT - Best Known (6, 43, s)-Nets in Base 27

Best Known (6, 43, s)-Nets in Base 27

(6, 43, 76)-Net over F₂₇ — Constructive and digital

Digital (6, 43, 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, 43, 626)-Net in Base 27 — Upper bound on s

There is no (6, 43, 627)-net in base 27, because

1 times m-reduction [i] would yield (6, 42, 627)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 340891 834257 631555 300203 551226 013626 022832 825471 922180 659765 > 27⁴² [i]