MinT - Best Known (80, 80+31, s)-Nets in Base 3

Best Known (80, 80+31, s)-Nets in Base 3

(80, 80+31, 228)-Net over F₃ — Constructive and digital

Digital (80, 111, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 37, 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]

(80, 80+31, 353)-Net over F₃ — Digital

Digital (80, 111, 353)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+31, 10115)-Net in Base 3 — Upper bound on s

There is no (80, 111, 10116)-net in base 3, because

1 times m-reduction [i] would yield (80, 110, 10116)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30437 427925 344650 217571 436890 486715 899994 902136 828465 > 3¹¹⁰ [i]