MinT - Best Known (29−25, 29, s)-Nets in Base 27

Best Known (29−25, 29, s)-Nets in Base 27

(29−25, 29, 64)-Net over F₂₇ — Constructive and digital

Digital (4, 29, 64)-net over F₂₇, using

net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
  - a function field by SÃ©mirat [i]

(29−25, 29, 438)-Net in Base 27 — Upper bound on s

There is no (4, 29, 439)-net in base 27, because

1 times m-reduction [i] would yield (4, 28, 439)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 11994 639614 520686 577217 478608 034822 639817 > 27²⁸ [i]