MinT - Best Known (53, 53+23, s)-Nets in Base 3

Best Known (53, 53+23, s)-Nets in Base 3

(53, 53+23, 144)-Net over F₃ — Constructive and digital

Digital (53, 76, 144)-net over F₃, using

3¹ times duplication [i] based on digital (52, 75, 144)-net over F₃, using
- trace code for nets [i] based on digital (2, 25, 48)-net over F₂₇, using
  - net from sequence [i] based on digital (2, 47)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
      - a function field by GarcÃa and Quoos [i]

(53, 53+23, 203)-Net over F₃ — Digital

Digital (53, 76, 203)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+23, 4385)-Net in Base 3 — Upper bound on s

There is no (53, 76, 4386)-net in base 3, because

1 times m-reduction [i] would yield (53, 75, 4386)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 608612 222417 798767 067856 679982 894081 > 3⁷⁵ [i]