MinT - Best Known (108−43, 108, s)-Nets in Base 3

Best Known (108−43, 108, s)-Nets in Base 3

(108−43, 108, 80)-Net over F₃ — Constructive and digital

Digital (65, 108, 80)-net over F₃, using

6 times m-reduction [i] based on digital (65, 114, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 57, 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]

(108−43, 108, 113)-Net over F₃ — Digital

Digital (65, 108, 113)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(108−43, 108, 1150)-Net in Base 3 — Upper bound on s

There is no (65, 108, 1151)-net in base 3, because

1 times m-reduction [i] would yield (65, 107, 1151)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1136 885130 915308 746681 862885 410488 372037 696577 225943 > 3¹⁰⁷ [i]