MinT - Best Known (163−73, 163, s)-Nets in Base 3

Best Known (163−73, 163, s)-Nets in Base 3

(163−73, 163, 80)-Net over F₃ — Constructive and digital

Digital (90, 163, 80)-net over F₃, using

1 times m-reduction [i] based on digital (90, 164, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 82, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(163−73, 163, 114)-Net over F₃ — Digital

Digital (90, 163, 114)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−73, 163, 966)-Net in Base 3 — Upper bound on s

There is no (90, 163, 967)-net in base 3, because

1 times m-reduction [i] would yield (90, 162, 967)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 198402 435925 151169 534350 884826 806943 080223 313678 290809 143258 109488 978146 756665 > 3¹⁶² [i]