MinT - Best Known (99−39, 99, s)-Nets in Base 3

Best Known (99−39, 99, s)-Nets in Base 3

(99−39, 99, 80)-Net over F₃ — Constructive and digital

Digital (60, 99, 80)-net over F₃, using

5 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]

(99−39, 99, 109)-Net over F₃ — Digital

Digital (60, 99, 109)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−39, 99, 1127)-Net in Base 3 — Upper bound on s

There is no (60, 99, 1128)-net in base 3, because

1 times m-reduction [i] would yield (60, 98, 1128)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 57768 468969 081621 802629 692141 630305 506641 808673 > 3⁹⁸ [i]