MinT - Best Known (230−55, 230, s)-Nets in Base 3

Best Known (230−55, 230, s)-Nets in Base 3

(230−55, 230, 464)-Net over F₃ — Constructive and digital

Digital (175, 230, 464)-net over F₃, using

3² times duplication [i] based on digital (173, 228, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 57, 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]

(230−55, 230, 1140)-Net over F₃ — Digital

Digital (175, 230, 1140)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−55, 230, 60797)-Net in Base 3 — Upper bound on s

There is no (175, 230, 60798)-net in base 3, because

1 times m-reduction [i] would yield (175, 229, 60798)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 236729 050047 176858 534826 221944 604764 758048 964554 991547 661767 325071 929104 134186 445571 161945 639206 721563 889425 > 3²²⁹ [i]