MinT - Best Known (68, 68+62, s)-Nets in Base 5

Best Known (68, 68+62, s)-Nets in Base 5

(68, 68+62, 104)-Net over F₅ — Constructive and digital

Digital (68, 130, 104)-net over F₅, using

trace code for nets [i] based on digital (3, 65, 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]

(68, 68+62, 152)-Net over F₅ — Digital

Digital (68, 130, 152)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+62, 2626)-Net in Base 5 — Upper bound on s

There is no (68, 130, 2627)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 376257 166153 415918 421443 349053 075563 052976 883396 866560 379112 844603 532637 478587 997441 885525 > 5¹³⁰ [i]