MinT - Best Known (213−52, 213, s)-Nets in Base 3

Best Known (213−52, 213, s)-Nets in Base 3

(213−52, 213, 400)-Net over F₃ — Constructive and digital

Digital (161, 213, 400)-net over F₃, using

3¹ times duplication [i] based on digital (160, 212, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 53, 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]

(213−52, 213, 984)-Net over F₃ — Digital

Digital (161, 213, 984)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(213−52, 213, 42729)-Net in Base 3 — Upper bound on s

There is no (161, 213, 42730)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 423595 084328 982722 952599 710583 302366 380278 690652 475694 033773 464401 621628 528054 929929 580138 976282 565941 > 3²¹³ [i]