MinT - Best Known (148−44, 148, s)-Nets in Base 5

Best Known (148−44, 148, s)-Nets in Base 5

(148−44, 148, 408)-Net over F₅ — Constructive and digital

Digital (104, 148, 408)-net over F₅, using

trace code for nets [i] based on digital (30, 74, 204)-net over F₂₅, using
- net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
    - a function field by GarcÃa and Quoos [i]

(148−44, 148, 1096)-Net over F₅ — Digital

Digital (104, 148, 1096)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−44, 148, 113997)-Net in Base 5 — Upper bound on s

There is no (104, 148, 113998)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 030649 653263 965917 863863 666689 207425 469726 939904 936449 831451 073677 514738 162752 599887 488545 893946 339521 > 5¹⁴⁸ [i]