MinT - Best Known (54−48, 54, s)-Nets in Base 27

Best Known (54−48, 54, s)-Nets in Base 27

(54−48, 54, 76)-Net over F₂₇ — Constructive and digital

Digital (6, 54, 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]

(54−48, 54, 612)-Net in Base 27 — Upper bound on s

There is no (6, 54, 613)-net in base 27, because

2 times m-reduction [i] would yield (6, 52, 613)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 271 938324 575646 848595 615128 543363 221547 752737 643934 131877 501219 467269 460707 > 27⁵² [i]