MinT - Best Known (94, 94+33, s)-Nets in Base 3

Best Known (94, 94+33, s)-Nets in Base 3

(94, 94+33, 264)-Net over F₃ — Constructive and digital

Digital (94, 127, 264)-net over F₃, using

3¹ times duplication [i] based on digital (93, 126, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 42, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(94, 94+33, 514)-Net over F₃ — Digital

Digital (94, 127, 514)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 94+33, 19430)-Net in Base 3 — Upper bound on s

There is no (94, 127, 19431)-net in base 3, because

1 times m-reduction [i] would yield (94, 126, 19431)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 310151 914765 301693 765556 220679 031732 881427 960887 904129 400033 > 3¹²⁶ [i]