MinT - Best Known (150−106, 150, s)-Nets in Base 5

Best Known (150−106, 150, s)-Nets in Base 5

(150−106, 150, 78)-Net over F₅ — Constructive and digital

Digital (44, 150, 78)-net over F₅, using

t-expansion [i] based on digital (38, 150, 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]

(150−106, 150, 84)-Net over F₅ — Digital

Digital (44, 150, 84)-net over F₅, using

t-expansion [i] based on digital (43, 150, 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]

(150−106, 150, 451)-Net in Base 5 — Upper bound on s

There is no (44, 150, 452)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 736 008211 578867 943120 836191 300403 388449 907102 727355 791785 395031 691817 683940 292298 970065 465306 147256 366225 > 5¹⁵⁰ [i]