MinT - Best Known (84, 84+31, s)-Nets in Base 3

Best Known (84, 84+31, s)-Nets in Base 3

(84, 84+31, 246)-Net over F₃ — Constructive and digital

Digital (84, 115, 246)-net over F₃, using

3¹ times duplication [i] based on digital (83, 114, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 38, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(84, 84+31, 414)-Net over F₃ — Digital

Digital (84, 115, 414)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+31, 13564)-Net in Base 3 — Upper bound on s

There is no (84, 115, 13565)-net in base 3, because

1 times m-reduction [i] would yield (84, 114, 13565)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 467197 437334 709444 454432 117079 140469 828443 396363 225691 > 3¹¹⁴ [i]