MinT - Best Known (55, 55+48, s)-Nets in Base 3

Best Known (55, 55+48, s)-Nets in Base 3

(55, 55+48, 56)-Net over F₃ — Constructive and digital

Digital (55, 103, 56)-net over F₃, using

1 times m-reduction [i] based on digital (55, 104, 56)-net over F₃, using
- trace code for nets [i] based on digital (3, 52, 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]

(55, 55+48, 70)-Net over F₃ — Digital

Digital (55, 103, 70)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+48, 523)-Net in Base 3 — Upper bound on s

There is no (55, 103, 524)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 975871 631271 865624 154684 179010 818526 398617 988673 > 3¹⁰³ [i]