MinT - Best Known (80, 113, s)-Nets in Base 3

Best Known (80, 113, s)-Nets in Base 3

(80, 113, 192)-Net over F₃ — Constructive and digital

Digital (80, 113, 192)-net over F₃, using

1 times m-reduction [i] based on digital (80, 114, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 38, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(80, 113, 304)-Net over F₃ — Digital

Digital (80, 113, 304)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 113, 7420)-Net in Base 3 — Upper bound on s

There is no (80, 113, 7421)-net in base 3, because

1 times m-reduction [i] would yield (80, 112, 7421)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 273996 505354 700990 506288 891508 813224 552667 055936 992193 > 3¹¹² [i]