MinT - Best Known (66, 66+60, s)-Nets in Base 5

Best Known (66, 66+60, s)-Nets in Base 5

(66, 66+60, 104)-Net over F₅ — Constructive and digital

Digital (66, 126, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 63, 52)-net over F₂₅, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by GarcÃa and Quoos [i]

(66, 66+60, 148)-Net over F₅ — Digital

Digital (66, 126, 148)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+60, 2574)-Net in Base 5 — Upper bound on s

There is no (66, 126, 2575)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 11802 243757 397284 188549 639174 105397 028271 067089 508098 472812 092069 116739 188349 107844 342153 > 5¹²⁶ [i]