MinT - Best Known (196−53, 196, s)-Nets in Base 3

Best Known (196−53, 196, s)-Nets in Base 3

(196−53, 196, 288)-Net over F₃ — Constructive and digital

Digital (143, 196, 288)-net over F₃, using

2 times m-reduction [i] based on digital (143, 198, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 66, 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]

(196−53, 196, 621)-Net over F₃ — Digital

Digital (143, 196, 621)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(196−53, 196, 19958)-Net in Base 3 — Upper bound on s

There is no (143, 196, 19959)-net in base 3, because

1 times m-reduction [i] would yield (143, 195, 19959)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1094 406439 878518 282308 191416 921210 593432 602290 656127 532742 656942 655857 082983 060202 669650 310461 > 3¹⁹⁵ [i]