MinT - Best Known (147−57, 147, s)-Nets in Base 3

Best Known (147−57, 147, s)-Nets in Base 3

(147−57, 147, 128)-Net over F₃ — Constructive and digital

Digital (90, 147, 128)-net over F₃, using

7 times m-reduction [i] based on digital (90, 154, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 77, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(147−57, 147, 157)-Net over F₃ — Digital

Digital (90, 147, 157)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−57, 147, 1709)-Net in Base 3 — Upper bound on s

There is no (90, 147, 1710)-net in base 3, because

1 times m-reduction [i] would yield (90, 146, 1710)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4584 917149 370202 263261 784655 023050 625552 019618 608673 065308 568741 003129 > 3¹⁴⁶ [i]