MinT - Best Known (112−32, 112, s)-Nets in Base 3

Best Known (112−32, 112, s)-Nets in Base 3

(112−32, 112, 204)-Net over F₃ — Constructive and digital

Digital (80, 112, 204)-net over F₃, using

3¹ times duplication [i] based on digital (79, 111, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 37, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(112−32, 112, 327)-Net over F₃ — Digital

Digital (80, 112, 327)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−32, 112, 7420)-Net in Base 3 — Upper bound on s

There is no (80, 112, 7421)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 273996 505354 700990 506288 891508 813224 552667 055936 992193 > 3¹¹² [i]