MinT - Best Known (107, 194, s)-Nets in Base 3

Best Known (107, 194, s)-Nets in Base 3

(107, 194, 80)-Net over F₃ — Constructive and digital

Digital (107, 194, 80)-net over F₃, using

4 times m-reduction [i] based on digital (107, 198, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 99, 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]

(107, 194, 132)-Net over F₃ — Digital

Digital (107, 194, 132)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 194, 1127)-Net in Base 3 — Upper bound on s

There is no (107, 194, 1128)-net in base 3, because

1 times m-reduction [i] would yield (107, 193, 1128)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 123 889200 537643 168841 631402 819219 288372 023726 991250 305070 977882 752907 708799 974117 458389 041441 > 3¹⁹³ [i]