MinT - Best Known (42−25, 42, s)-Nets in Base 3

Best Known (42−25, 42, s)-Nets in Base 3

(42−25, 42, 28)-Net over F₃ — Constructive and digital

Digital (17, 42, 28)-net over F₃, using

t-expansion [i] based on digital (15, 42, 28)-net over F₃, using
- net from sequence [i] based on digital (15, 27)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(42−25, 42, 101)-Net in Base 3 — Upper bound on s

There is no (17, 42, 102)-net in base 3, because

1 times m-reduction [i] would yield (17, 41, 102)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 37 195603 054569 594969 > 3⁴¹ [i]