MinT - Best Known (120, 233, s)-Nets in Base 3

Best Known (120, 233, s)-Nets in Base 3

(120, 233, 77)-Net over F₃ — Constructive and digital

Digital (120, 233, 77)-net over F₃, using

net from sequence [i] based on digital (120, 76)-sequence over F₃, using
- base reduction for sequences [i] based on digital (22, 76)-sequence over F₉, using
  - s-reduction based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(120, 233, 125)-Net over F₃ — Digital

Digital (120, 233, 125)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 233, 974)-Net in Base 3 — Upper bound on s

There is no (120, 233, 975)-net in base 3, because

1 times m-reduction [i] would yield (120, 232, 975)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 510 367637 914452 821449 754147 813819 790290 490853 987693 390475 924061 993103 865981 621569 416644 779395 404644 282544 763537 > 3²³² [i]