MinT - Best Known (10, 10+27, s)-Nets in Base 5

Best Known (10, 10+27, s)-Nets in Base 5

(10, 10+27, 26)-Net over F₅ — Constructive and digital

Digital (10, 37, 26)-net over F₅, using

t-expansion [i] based on digital (9, 37, 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]

(10, 10+27, 27)-Net over F₅ — Digital

Digital (10, 37, 27)-net over F₅, using

net from sequence [i] based on digital (10, 26)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 10 and N(F) ≥ 27, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(10, 10+27, 113)-Net in Base 5 — Upper bound on s

There is no (10, 37, 114)-net in base 5, because

1 times m-reduction [i] would yield (10, 36, 114)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 15 900680 596429 283395 677129 > 5³⁶ [i]