MinT - Best Known (105−66, 105, s)-Nets in Base 5

Best Known (105−66, 105, s)-Nets in Base 5

(105−66, 105, 78)-Net over F₅ — Constructive and digital

Digital (39, 105, 78)-net over F₅, using

t-expansion [i] based on digital (38, 105, 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]

(105−66, 105, 527)-Net in Base 5 — Upper bound on s

There is no (39, 105, 528)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 25 709192 023748 444065 214808 920275 073741 140826 324460 378907 932112 306108 610625 > 5¹⁰⁵ [i]