MinT - Best Known (72, 99, s)-Nets in Base 3

Best Known (72, 99, s)-Nets in Base 3

(72, 99, 228)-Net over F₃ — Constructive and digital

Digital (72, 99, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 33, 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]

(72, 99, 357)-Net over F₃ — Digital

Digital (72, 99, 357)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 99, 11185)-Net in Base 3 — Upper bound on s

There is no (72, 99, 11186)-net in base 3, because

1 times m-reduction [i] would yield (72, 98, 11186)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 57303 979989 560819 155443 927341 445356 148357 533229 > 3⁹⁸ [i]