MinT - Best Known (150−46, 150, s)-Nets in Base 5

Best Known (150−46, 150, s)-Nets in Base 5

(150−46, 150, 400)-Net over F₅ — Constructive and digital

Digital (104, 150, 400)-net over F₅, using

t-expansion [i] based on digital (100, 150, 400)-net over F₅, using
- trace code for nets [i] based on digital (25, 75, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(150−46, 150, 964)-Net over F₅ — Digital

Digital (104, 150, 964)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−46, 150, 85272)-Net in Base 5 — Upper bound on s

There is no (104, 150, 85273)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 700 668487 967418 326219 680318 787647 290484 235459 429690 743756 806593 699725 837491 979232 162212 878502 926552 591565 > 5¹⁵⁰ [i]