MinT - Best Known (102−26, 102, s)-Nets in Base 3

Best Known (102−26, 102, s)-Nets in Base 3

(102−26, 102, 252)-Net over F₃ — Constructive and digital

Digital (76, 102, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 34, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(102−26, 102, 462)-Net over F₃ — Digital

Digital (76, 102, 462)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−26, 102, 15689)-Net in Base 3 — Upper bound on s

There is no (76, 102, 15690)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 641972 412198 528023 254632 756821 560616 216288 464157 > 3¹⁰² [i]