MinT - Best Known (154, 154+50, s)-Nets in Base 3

Best Known (154, 154+50, s)-Nets in Base 3

(154, 154+50, 400)-Net over F₃ — Constructive and digital

Digital (154, 204, 400)-net over F₃, using

trace code for nets [i] based on digital (1, 51, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(154, 154+50, 935)-Net over F₃ — Digital

Digital (154, 204, 935)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(154, 154+50, 39777)-Net in Base 3 — Upper bound on s

There is no (154, 204, 39778)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 520941 585674 053727 884365 312250 429612 793162 029531 844029 351083 703142 807843 656517 770345 186225 445205 > 3²⁰⁴ [i]