MinT - Best Known (127−89, 127, s)-Nets in Base 5

Best Known (127−89, 127, s)-Nets in Base 5

(127−89, 127, 78)-Net over F₅ — Constructive and digital

Digital (38, 127, 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]

(127−89, 127, 401)-Net in Base 5 — Upper bound on s

There is no (38, 127, 402)-net in base 5, because

1 times m-reduction [i] would yield (38, 126, 402)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 12611 198194 305313 199530 968926 309904 565843 901627 877413 093445 860934 636396 905469 652574 002625 > 5¹²⁶ [i]