MinT - Best Known (52, 75, s)-Nets in Base 3

Best Known (52, 75, s)-Nets in Base 3

(52, 75, 144)-Net over F₃ — Constructive and digital

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]

(52, 75, 192)-Net over F₃ — Digital

Digital (52, 75, 192)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 75, 3967)-Net in Base 3 — Upper bound on s

There is no (52, 75, 3968)-net in base 3, because

1 times m-reduction [i] would yield (52, 74, 3968)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 202802 488834 954302 334007 312702 586369 > 3⁷⁴ [i]