MinT - Best Known (177−52, 177, s)-Nets in Base 3

Best Known (177−52, 177, s)-Nets in Base 3

(177−52, 177, 246)-Net over F₃ — Constructive and digital

Digital (125, 177, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 59, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(177−52, 177, 427)-Net over F₃ — Digital

Digital (125, 177, 427)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−52, 177, 9314)-Net in Base 3 — Upper bound on s

There is no (125, 177, 9315)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 823247 622171 739123 987758 849245 201996 122853 418103 031686 513571 957059 370491 095637 195637 > 3¹⁷⁷ [i]