MinT - Best Known (137, 137+52, s)-Nets in Base 3

Best Known (137, 137+52, s)-Nets in Base 3

(137, 137+52, 288)-Net over F₃ — Constructive and digital

Digital (137, 189, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 63, 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]

(137, 137+52, 566)-Net over F₃ — Digital

Digital (137, 189, 566)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+52, 15482)-Net in Base 3 — Upper bound on s

There is no (137, 189, 15483)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 499556 253014 592457 465132 619628 330469 255438 064675 724028 032550 789805 560525 062736 941982 353317 > 3¹⁸⁹ [i]