MinT - Best Known (65, 65+80, s)-Nets in Base 5

Best Known (65, 65+80, s)-Nets in Base 5

(65, 65+80, 82)-Net over F₅ — Constructive and digital

Digital (65, 145, 82)-net over F₅, using

t-expansion [i] based on digital (48, 145, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(65, 65+80, 120)-Net over F₅ — Digital

Digital (65, 145, 120)-net over F₅, using

t-expansion [i] based on digital (61, 145, 120)-net over F₅, using
- net from sequence [i] based on digital (61, 119)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 61 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(65, 65+80, 1318)-Net in Base 5 — Upper bound on s

There is no (65, 145, 1319)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 230069 477191 739651 080327 608423 006097 689146 310952 564252 581741 478323 979902 917708 602099 911250 634788 210017 > 5¹⁴⁵ [i]