MinT - Best Known (146−38, 146, s)-Nets in Base 5

Best Known (146−38, 146, s)-Nets in Base 5

(146−38, 146, 416)-Net over F₅ — Constructive and digital

Digital (108, 146, 416)-net over F₅, using

trace code for nets [i] based on digital (35, 73, 208)-net over F₂₅, using
- net from sequence [i] based on digital (35, 207)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 35 and N(F) ≥ 208, using
    - a function field by GarcÃa and Quoos [i]

(146−38, 146, 2117)-Net over F₅ — Digital

Digital (108, 146, 2117)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−38, 146, 465774)-Net in Base 5 — Upper bound on s

There is no (108, 146, 465775)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 121078 738824 767469 061596 991183 176754 199408 490268 740718 032512 051134 830453 709929 096097 564010 309113 775221 > 5¹⁴⁶ [i]