MinT - Best Known (11, 11+41, s)-Nets in Base 27

Best Known (11, 11+41, s)-Nets in Base 27

(11, 11+41, 96)-Net over F₂₇ — Constructive and digital

Digital (11, 52, 96)-net over F₂₇, using

net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
  - an explicitly constructive algebraic function field [i]

(11, 11+41, 100)-Net over F₂₇ — Digital

Digital (11, 52, 100)-net over F₂₇, using

net from sequence [i] based on digital (11, 99)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 100, using
  - a curve from the manYPoints database [i]

(11, 11+41, 1416)-Net in Base 27 — Upper bound on s

There is no (11, 52, 1417)-net in base 27, because

1 times m-reduction [i] would yield (11, 51, 1417)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 10 077604 464487 212458 997979 570951 670612 458420 397760 495191 049129 128712 734577 > 27⁵¹ [i]