MinT - Best Known (101−41, 101, s)-Nets in Base 3

Best Known (101−41, 101, s)-Nets in Base 3

(101−41, 101, 80)-Net over F₃ — Constructive and digital

Digital (60, 101, 80)-net over F₃, using

3 times m-reduction [i] based on digital (60, 104, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 52, 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]

(101−41, 101, 102)-Net over F₃ — Digital

Digital (60, 101, 102)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−41, 101, 989)-Net in Base 3 — Upper bound on s

There is no (60, 101, 990)-net in base 3, because

1 times m-reduction [i] would yield (60, 100, 990)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 519109 986152 221023 143564 800507 006103 253453 547689 > 3¹⁰⁰ [i]