MinT - Best Known (119−83, 119, s)-Nets in Base 5

Best Known (119−83, 119, s)-Nets in Base 5

(119−83, 119, 72)-Net over F₅ — Constructive and digital

Digital (36, 119, 72)-net over F₅, using

t-expansion [i] based on digital (31, 119, 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]

(119−83, 119, 76)-Net over F₅ — Digital

Digital (36, 119, 76)-net over F₅, using

t-expansion [i] based on digital (34, 119, 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]

(119−83, 119, 385)-Net in Base 5 — Upper bound on s

There is no (36, 119, 386)-net in base 5, because

1 times m-reduction [i] would yield (36, 118, 386)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 33196 808953 080605 971721 331853 349941 424731 335041 813822 338325 234624 941915 431039 951625 > 5¹¹⁸ [i]