MinT - Best Known (82, 82+31, s)-Nets in Base 3

Best Known (82, 82+31, s)-Nets in Base 3

(82, 82+31, 228)-Net over F₃ — Constructive and digital

Digital (82, 113, 228)-net over F₃, using

1 times m-reduction [i] based on digital (82, 114, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 38, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(82, 82+31, 382)-Net over F₃ — Digital

Digital (82, 113, 382)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+31, 11713)-Net in Base 3 — Upper bound on s

There is no (82, 113, 11714)-net in base 3, because

1 times m-reduction [i] would yield (82, 112, 11714)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 273894 453677 815051 808267 962867 377573 906170 147791 089561 > 3¹¹² [i]