MinT - Best Known (150−56, 150, s)-Nets in Base 5

Best Known (150−56, 150, s)-Nets in Base 5

(150−56, 150, 296)-Net over F₅ — Constructive and digital

Digital (94, 150, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 75, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(150−56, 150, 414)-Net over F₅ — Digital

Digital (94, 150, 414)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−56, 150, 15662)-Net in Base 5 — Upper bound on s

There is no (94, 150, 15663)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 701 350576 607019 564782 302920 432944 499296 861917 005874 735621 349161 719045 527461 037593 316146 288669 273669 986705 > 5¹⁵⁰ [i]