MinT - Best Known (72, 72+54, s)-Nets in Base 3

Best Known (72, 72+54, s)-Nets in Base 3

(72, 72+54, 80)-Net over F₃ — Constructive and digital

Digital (72, 126, 80)-net over F₃, using

2 times m-reduction [i] based on digital (72, 128, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 64, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(72, 72+54, 104)-Net over F₃ — Digital

Digital (72, 126, 104)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+54, 894)-Net in Base 3 — Upper bound on s

There is no (72, 126, 895)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 343411 869297 067410 110644 726140 353595 806362 866870 018154 364363 > 3¹²⁶ [i]