MinT - Best Known (20−11, 20, s)-Nets in Base 5

Best Known (20−11, 20, s)-Nets in Base 5

(20−11, 20, 26)-Net over F₅ — Constructive and digital

Digital (9, 20, 26)-net over F₅, using

net from sequence [i] based on digital (9, 25)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 9 and N(F) ≥ 26, using
  - an explicitly constructive algebraic function field [i]

(20−11, 20, 27)-Net over F₅ — Digital

Digital (9, 20, 27)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(20−11, 20, 291)-Net in Base 5 — Upper bound on s

There is no (9, 20, 292)-net in base 5, because

1 times m-reduction [i] would yield (9, 19, 292)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 19 141055 119377 > 5¹⁹ [i]