MinT - Best Known (139, 139+53, s)-Nets in Base 3

Best Known (139, 139+53, s)-Nets in Base 3

(139, 139+53, 288)-Net over F₃ — Constructive and digital

Digital (139, 192, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 64, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(139, 139+53, 567)-Net over F₃ — Digital

Digital (139, 192, 567)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(139, 139+53, 16850)-Net in Base 3 — Upper bound on s

There is no (139, 192, 16851)-net in base 3, because

1 times m-reduction [i] would yield (139, 191, 16851)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 504921 629425 131170 262744 364964 361840 376431 674053 562350 897321 124975 721371 319861 823520 059733 > 3¹⁹¹ [i]