MinT - Best Known (103, 103+77, s)-Nets in Base 3

Best Known (103, 103+77, s)-Nets in Base 3

(103, 103+77, 128)-Net over F₃ — Constructive and digital

Digital (103, 180, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 90, 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]

(103, 103+77, 141)-Net over F₃ — Digital

Digital (103, 180, 141)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 103+77, 1291)-Net in Base 3 — Upper bound on s

There is no (103, 180, 1292)-net in base 3, because

1 times m-reduction [i] would yield (103, 179, 1292)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 26 024122 153982 898014 938113 808896 476288 391971 992480 060979 521897 627832 234634 127548 135945 > 3¹⁷⁹ [i]