MinT - Best Known (76, 76+51, s)-Nets in Base 3

Best Known (76, 76+51, s)-Nets in Base 3

(76, 76+51, 80)-Net over F₃ — Constructive and digital

Digital (76, 127, 80)-net over F₃, using

9 times m-reduction [i] based on digital (76, 136, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 68, 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]

(76, 76+51, 126)-Net over F₃ — Digital

Digital (76, 127, 126)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+51, 1267)-Net in Base 3 — Upper bound on s

There is no (76, 127, 1268)-net in base 3, because

1 times m-reduction [i] would yield (76, 126, 1268)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 315992 389077 817452 571948 081243 508167 627239 778624 350370 189033 > 3¹²⁶ [i]