MinT - Best Known (152, 219, s)-Nets in Base 3

Best Known (152, 219, s)-Nets in Base 3

(152, 219, 228)-Net over F₃ — Constructive and digital

Digital (152, 219, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 73, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(152, 219, 451)-Net over F₃ — Digital

Digital (152, 219, 451)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(152, 219, 9304)-Net in Base 3 — Upper bound on s

There is no (152, 219, 9305)-net in base 3, because

1 times m-reduction [i] would yield (152, 218, 9305)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 103 001146 249894 925542 123223 293987 621960 462328 174812 557855 005933 560693 496915 425787 092208 953384 018906 554931 > 3²¹⁸ [i]