MinT - Best Known (102, 102+81, s)-Nets in Base 3

Best Known (102, 102+81, s)-Nets in Base 3

(102, 102+81, 80)-Net over F₃ — Constructive and digital

Digital (102, 183, 80)-net over F₃, using

5 times m-reduction [i] based on digital (102, 188, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 94, 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]

(102, 102+81, 130)-Net over F₃ — Digital

Digital (102, 183, 130)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+81, 1129)-Net in Base 3 — Upper bound on s

There is no (102, 183, 1130)-net in base 3, because

1 times m-reduction [i] would yield (102, 182, 1130)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 694 124812 482284 210758 870209 989599 166087 589171 017190 256365 481919 068079 004536 402380 450321 > 3¹⁸² [i]