MinT - Best Known (213−50, 213, s)-Nets in Base 3

Best Known (213−50, 213, s)-Nets in Base 3

(213−50, 213, 464)-Net over F₃ — Constructive and digital

Digital (163, 213, 464)-net over F₃, using

3¹ times duplication [i] based on digital (162, 212, 464)-net over F₃, using
- t-expansion [i] based on digital (161, 212, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 53, 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]

(213−50, 213, 1157)-Net over F₃ — Digital

Digital (163, 213, 1157)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−50, 213, 59086)-Net in Base 3 — Upper bound on s

There is no (163, 213, 59087)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 423548 291458 096220 504169 328594 781495 430062 972303 148914 977627 078386 027266 452386 433908 190761 524950 196079 > 3²¹³ [i]