MinT - Best Known (193−43, 193, s)-Nets in Base 3

Best Known (193−43, 193, s)-Nets in Base 3

(193−43, 193, 640)-Net over F₃ — Constructive and digital

Digital (150, 193, 640)-net over F₃, using

3¹ times duplication [i] based on digital (149, 192, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 48, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(193−43, 193, 1307)-Net over F₃ — Digital

Digital (150, 193, 1307)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−43, 193, 99913)-Net in Base 3 — Upper bound on s

There is no (150, 193, 99914)-net in base 3, because

1 times m-reduction [i] would yield (150, 192, 99914)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 486492 977965 078742 197559 008392 921205 480771 944300 543997 474832 064483 008513 592920 107146 699341 > 3¹⁹² [i]