MinT - Best Known (152, 200, s)-Nets in Base 3

Best Known (152, 200, s)-Nets in Base 3

(152, 200, 464)-Net over F₃ — Constructive and digital

Digital (152, 200, 464)-net over F₃, using

trace code for nets [i] based on digital (2, 50, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(152, 200, 1003)-Net over F₃ — Digital

Digital (152, 200, 1003)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(152, 200, 46357)-Net in Base 3 — Upper bound on s

There is no (152, 200, 46358)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 265636 691687 306945 308495 330282 293608 616926 877050 296528 112683 521161 738065 902521 991348 637557 359473 > 3²⁰⁰ [i]