MinT - Best Known (228−53, 228, s)-Nets in Base 3

Best Known (228−53, 228, s)-Nets in Base 3

(228−53, 228, 600)-Net over F₃ — Constructive and digital

Digital (175, 228, 600)-net over F₃, using

trace code for nets [i] based on digital (4, 57, 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]

(228−53, 228, 1274)-Net over F₃ — Digital

Digital (175, 228, 1274)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−53, 228, 77224)-Net in Base 3 — Upper bound on s

There is no (175, 228, 77225)-net in base 3, because

1 times m-reduction [i] would yield (175, 227, 77225)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 025788 594049 198657 440380 790167 135213 068079 013566 829867 088424 052943 667283 752473 340094 884982 110798 989892 925049 > 3²²⁷ [i]