MinT - Best Known (88−41, 88, s)-Nets in Base 3

Best Known (88−41, 88, s)-Nets in Base 3

(88−41, 88, 56)-Net over F₃ — Constructive and digital

Digital (47, 88, 56)-net over F₃, using

trace code for nets [i] based on digital (3, 44, 28)-net over F₉, using
- net from sequence [i] based on digital (3, 27)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
    - the Hermitian function field over F₉ [i]

(88−41, 88, 62)-Net over F₃ — Digital

Digital (47, 88, 62)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−41, 88, 474)-Net in Base 3 — Upper bound on s

There is no (47, 88, 475)-net in base 3, because

1 times m-reduction [i] would yield (47, 87, 475)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 325283 654973 463759 899651 547180 044892 120761 > 3⁸⁷ [i]