MinT - Best Known (105, 105+89, s)-Nets in Base 3

Best Known (105, 105+89, s)-Nets in Base 3

(105, 105+89, 80)-Net over F₃ — Constructive and digital

Digital (105, 194, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 97, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(105, 105+89, 124)-Net over F₃ — Digital

Digital (105, 194, 124)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+89, 1025)-Net in Base 3 — Upper bound on s

There is no (105, 194, 1026)-net in base 3, because

1 times m-reduction [i] would yield (105, 193, 1026)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 123 526677 807954 448873 786863 395876 249475 621445 037773 012118 852418 033798 834153 137296 435993 420985 > 3¹⁹³ [i]