MinT - Best Known (238−106, 238, s)-Nets in Base 3

Best Known (238−106, 238, s)-Nets in Base 3

(238−106, 238, 128)-Net over F₃ — Constructive and digital

Digital (132, 238, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 119, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(238−106, 238, 161)-Net over F₃ — Digital

Digital (132, 238, 161)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(238−106, 238, 1378)-Net in Base 3 — Upper bound on s

There is no (132, 238, 1379)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 369777 015724 955774 607380 018905 901375 526636 223814 862319 137287 739621 540197 236530 997623 704731 226789 440579 704550 048095 > 3²³⁸ [i]