MinT - Best Known (152, 152+49, s)-Nets in Base 3

Best Known (152, 152+49, s)-Nets in Base 3

(152, 152+49, 400)-Net over F₃ — Constructive and digital

Digital (152, 201, 400)-net over F₃, using

3¹ times duplication [i] based on digital (151, 200, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 50, 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]

(152, 152+49, 944)-Net over F₃ — Digital

Digital (152, 201, 944)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(152, 152+49, 46357)-Net in Base 3 — Upper bound on s

There is no (152, 201, 46358)-net in base 3, because

1 times m-reduction [i] would yield (152, 200, 46358)-net in base 3, but
- 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]