MinT - Best Known (202−46, 202, s)-Nets in Base 3

Best Known (202−46, 202, s)-Nets in Base 3

(202−46, 202, 600)-Net over F₃ — Constructive and digital

Digital (156, 202, 600)-net over F₃, using

3² times duplication [i] based on digital (154, 200, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 50, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(202−46, 202, 1244)-Net over F₃ — Digital

Digital (156, 202, 1244)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−46, 202, 73057)-Net in Base 3 — Upper bound on s

There is no (156, 202, 73058)-net in base 3, because

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]