MinT - Best Known (156, 203, s)-Nets in Base 3

Best Known (156, 203, s)-Nets in Base 3

(156, 203, 464)-Net over F₃ — Constructive and digital

Digital (156, 203, 464)-net over F₃, using

t-expansion [i] based on digital (155, 203, 464)-net over F₃, using
- 1 times m-reduction [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]

(156, 203, 1170)-Net over F₃ — Digital

Digital (156, 203, 1170)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(156, 203, 73057)-Net in Base 3 — Upper bound on s

There is no (156, 203, 73058)-net in base 3, because

1 times m-reduction [i] would yield (156, 202, 73058)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 391276 559138 619141 554880 719847 583948 856191 632283 827724 451289 398987 427578 344366 794213 958901 232457 > 3²⁰² [i]