MinT - Best Known (68−46, 68, s)-Nets in Base 5

Best Known (68−46, 68, s)-Nets in Base 5

(68−46, 68, 51)-Net over F₅ — Constructive and digital

Digital (22, 68, 51)-net over F₅, using

net from sequence [i] based on digital (22, 50)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
  - an explicitly constructive algebraic function field [i]

(68−46, 68, 258)-Net in Base 5 — Upper bound on s

There is no (22, 68, 259)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 357945 386127 220179 453767 669364 916530 009674 820725 > 5⁶⁸ [i]