MinT - Best Known (110−36, 110, s)-Nets in Base 5

Best Known (110−36, 110, s)-Nets in Base 5

(110−36, 110, 296)-Net over F₅ — Constructive and digital

Digital (74, 110, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 55, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(110−36, 110, 564)-Net over F₅ — Digital

Digital (74, 110, 564)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(110−36, 110, 35269)-Net in Base 5 — Upper bound on s

There is no (74, 110, 35270)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 77075 708120 490782 340103 212813 408357 785368 563613 719320 867116 718095 161374 410369 > 5¹¹⁰ [i]