MinT - Best Known (114−71, 114, s)-Nets in Base 5

Best Known (114−71, 114, s)-Nets in Base 5

(114−71, 114, 78)-Net over F₅ — Constructive and digital

Digital (43, 114, 78)-net over F₅, using

t-expansion [i] based on digital (38, 114, 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]

(114−71, 114, 84)-Net over F₅ — Digital

Digital (43, 114, 84)-net over F₅, using

net from sequence [i] based on digital (43, 83)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 43 and N(F) ≥ 84, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(114−71, 114, 602)-Net in Base 5 — Upper bound on s

There is no (43, 114, 603)-net in base 5, because

1 times m-reduction [i] would yield (43, 113, 603)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9 900560 297409 560472 748106 469582 333774 661297 828612 565166 164752 350651 007826 298405 > 5¹¹³ [i]