MinT - Best Known (243−73, 243, s)-Nets in Base 3

Best Known (243−73, 243, s)-Nets in Base 3

(243−73, 243, 252)-Net over F₃ — Constructive and digital

Digital (170, 243, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 81, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(243−73, 243, 523)-Net over F₃ — Digital

Digital (170, 243, 523)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−73, 243, 11473)-Net in Base 3 — Upper bound on s

There is no (170, 243, 11474)-net in base 3, because

1 times m-reduction [i] would yield (170, 242, 11474)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 141716 566674 476398 315601 942647 111835 016502 904775 101045 157066 277954 962014 506827 797879 381714 080445 304419 105291 997801 > 3²⁴² [i]