MinT - Best Known (121, 238, s)-Nets in Base 3

Best Known (121, 238, s)-Nets in Base 3

(121, 238, 78)-Net over F₃ — Constructive and digital

Digital (121, 238, 78)-net over F₃, using

net from sequence [i] based on digital (121, 77)-sequence over F₃, using
- base reduction for sequences [i] 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]

(121, 238, 122)-Net over F₃ — Digital

Digital (121, 238, 122)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 238, 943)-Net in Base 3 — Upper bound on s

There is no (121, 238, 944)-net in base 3, because

1 times m-reduction [i] would yield (121, 237, 944)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 123794 728791 713350 988613 152027 650907 085900 305460 067810 404503 505831 623341 228987 059827 009591 028478 150501 505101 039905 > 3²³⁷ [i]