MinT - Best Known (122, 122+55, s)-Nets in Base 3

Best Known (122, 122+55, s)-Nets in Base 3

(122, 122+55, 192)-Net over F₃ — Constructive and digital

Digital (122, 177, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 59, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(122, 122+55, 357)-Net over F₃ — Digital

Digital (122, 177, 357)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(122, 122+55, 7012)-Net in Base 3 — Upper bound on s

There is no (122, 177, 7013)-net in base 3, because

1 times m-reduction [i] would yield (122, 176, 7013)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 942728 695717 035453 282762 629513 242530 706609 528892 110815 316983 245708 059960 634867 759051 > 3¹⁷⁶ [i]