MinT - Best Known (23−20, 23, s)-Nets in Base 9

Best Known (23−20, 23, s)-Nets in Base 9

(23−20, 23, 28)-Net over F₉ — Constructive and digital

Digital (3, 23, 28)-net over F₉, using

net from sequence [i] based on digital (3, 27)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
  - the Hermitian function field over F₉ [i]

(23−20, 23, 82)-Net in Base 9 — Upper bound on s

There is no (3, 23, 83)-net in base 9, because

2 times m-reduction [i] would yield (3, 21, 83)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 117 432303 670953 710937 > 9²¹ [i]