MinT - Best Known (146−99, 146, s)-Nets in Base 5

Best Known (146−99, 146, s)-Nets in Base 5

(146−99, 146, 78)-Net over F₅ — Constructive and digital

Digital (47, 146, 78)-net over F₅, using

t-expansion [i] based on digital (38, 146, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(146−99, 146, 92)-Net over F₅ — Digital

Digital (47, 146, 92)-net over F₅, using

net from sequence [i] based on digital (47, 91)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 47 and N(F) ≥ 92, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(146−99, 146, 523)-Net in Base 5 — Upper bound on s

There is no (47, 146, 524)-net in base 5, because

1 times m-reduction [i] would yield (47, 145, 524)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 227389 905609 832076 656215 729484 042089 039300 809469 154169 075702 100604 251660 094086 051989 468916 838443 455025 > 5¹⁴⁵ [i]