MinT - Best Known (121−45, 121, s)-Nets in Base 3

Best Known (121−45, 121, s)-Nets in Base 3

(121−45, 121, 128)-Net over F₃ — Constructive and digital

Digital (76, 121, 128)-net over F₃, using

5 times m-reduction [i] based on digital (76, 126, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 63, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(121−45, 121, 151)-Net over F₃ — Digital

Digital (76, 121, 151)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−45, 121, 1791)-Net in Base 3 — Upper bound on s

There is no (76, 121, 1792)-net in base 3, because

1 times m-reduction [i] would yield (76, 120, 1792)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1814 351606 243262 641083 905257 275603 337518 190457 010453 064193 > 3¹²⁰ [i]