MinT - Best Known (32−17, 32, s)-Nets in Base 3

Best Known (32−17, 32, s)-Nets in Base 3

(32−17, 32, 28)-Net over F₃ — Constructive and digital

Digital (15, 32, 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]

(32−17, 32, 125)-Net in Base 3 — Upper bound on s

There is no (15, 32, 126)-net in base 3, because

1 times m-reduction [i] would yield (15, 31, 126)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 633 976257 710161 > 3³¹ [i]