MinT - Best Known (130−38, 130, s)-Nets in Base 3

Best Known (130−38, 130, s)-Nets in Base 3

(130−38, 130, 204)-Net over F₃ — Constructive and digital

Digital (92, 130, 204)-net over F₃, using

3¹ times duplication [i] based on digital (91, 129, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 43, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(130−38, 130, 338)-Net over F₃ — Digital

Digital (92, 130, 338)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−38, 130, 7271)-Net in Base 3 — Upper bound on s

There is no (92, 130, 7272)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 106 375609 069264 986847 633278 120757 246764 456991 433891 679021 821217 > 3¹³⁰ [i]