MinT - Best Known (205−49, 205, s)-Nets in Base 3

Best Known (205−49, 205, s)-Nets in Base 3

(205−49, 205, 464)-Net over F₃ — Constructive and digital

Digital (156, 205, 464)-net over F₃, using

3¹ times duplication [i] based on digital (155, 204, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 51, 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]

(205−49, 205, 1040)-Net over F₃ — Digital

Digital (156, 205, 1040)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−49, 205, 55677)-Net in Base 3 — Upper bound on s

There is no (156, 205, 55678)-net in base 3, because

1 times m-reduction [i] would yield (156, 204, 55678)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 518838 367292 013633 998295 150679 803104 549698 389044 662181 151571 679572 600880 674769 009625 412299 992049 > 3²⁰⁴ [i]