MinT - Best Known (115, 154, s)-Nets in Base 3

Best Known (115, 154, s)-Nets in Base 3

(115, 154, 288)-Net over F₃ — Constructive and digital

Digital (115, 154, 288)-net over F₃, using

2 times m-reduction [i] based on digital (115, 156, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 52, 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]

(115, 154, 657)-Net over F₃ — Digital

Digital (115, 154, 657)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 154, 27540)-Net in Base 3 — Upper bound on s

There is no (115, 154, 27541)-net in base 3, because

1 times m-reduction [i] would yield (115, 153, 27541)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 991463 091385 015650 744127 723525 072320 062919 268870 878085 250615 127071 325675 > 3¹⁵³ [i]