MinT - Best Known (116−82, 116, s)-Nets in Base 5

Best Known (116−82, 116, s)-Nets in Base 5

(116−82, 116, 72)-Net over F₅ — Constructive and digital

Digital (34, 116, 72)-net over F₅, using

t-expansion [i] based on digital (31, 116, 72)-net over F₅, using
- net from sequence [i] based on digital (31, 71)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
    - an explicitly constructive algebraic function field [i]

(116−82, 116, 76)-Net over F₅ — Digital

Digital (34, 116, 76)-net over F₅, using

net from sequence [i] based on digital (34, 75)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 34 and N(F) ≥ 76, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(116−82, 116, 353)-Net in Base 5 — Upper bound on s

There is no (34, 116, 354)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1233 668340 983722 178289 263938 086252 810630 344487 301693 374980 976393 841804 323648 445065 > 5¹¹⁶ [i]