MinT - Best Known (117−70, 117, s)-Nets in Base 5

Best Known (117−70, 117, s)-Nets in Base 5

(117−70, 117, 78)-Net over F₅ — Constructive and digital

Digital (47, 117, 78)-net over F₅, using

t-expansion [i] based on digital (38, 117, 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]

(117−70, 117, 92)-Net over F₅ — Digital

Digital (47, 117, 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]

(117−70, 117, 729)-Net in Base 5 — Upper bound on s

There is no (47, 117, 730)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6235 881474 506130 491221 615156 217622 841489 923431 027946 302205 470633 966090 766366 884105 > 5¹¹⁷ [i]