MinT - Best Known (150−51, 150, s)-Nets in Base 5

Best Known (150−51, 150, s)-Nets in Base 5

(150−51, 150, 296)-Net over F₅ — Constructive and digital

Digital (99, 150, 296)-net over F₅, using

t-expansion [i] based on 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]

(150−51, 150, 607)-Net over F₅ — Digital

Digital (99, 150, 607)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−51, 150, 37257)-Net in Base 5 — Upper bound on s

There is no (99, 150, 37258)-net in base 5, because

1 times m-reduction [i] would yield (99, 149, 37258)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 171126 162164 800146 535664 321284 395550 284160 713023 901841 847239 653671 997297 895517 757821 027226 726547 174185 > 5¹⁴⁹ [i]