MinT - Best Known (116−66, 116, s)-Nets in Base 5

Best Known (116−66, 116, s)-Nets in Base 5

(116−66, 116, 82)-Net over F₅ — Constructive and digital

Digital (50, 116, 82)-net over F₅, using

t-expansion [i] based on digital (48, 116, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(116−66, 116, 96)-Net over F₅ — Digital

Digital (50, 116, 96)-net over F₅, using

t-expansion [i] based on digital (49, 116, 96)-net over F₅, using
- net from sequence [i] based on digital (49, 95)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 49 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(116−66, 116, 918)-Net in Base 5 — Upper bound on s

There is no (50, 116, 919)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1226 400497 496114 142617 755519 553337 256805 080369 819794 171881 751600 054502 657813 130717 > 5¹¹⁶ [i]