MinT - Best Known (108−62, 108, s)-Nets in Base 5

Best Known (108−62, 108, s)-Nets in Base 5

(108−62, 108, 78)-Net over F₅ — Constructive and digital

Digital (46, 108, 78)-net over F₅, using

t-expansion [i] based on digital (38, 108, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(108−62, 108, 88)-Net over F₅ — Digital

Digital (46, 108, 88)-net over F₅, using

t-expansion [i] based on digital (45, 108, 88)-net over F₅, using
- net from sequence [i] based on digital (45, 87)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 45 and N(F) ≥ 88, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(108−62, 108, 822)-Net in Base 5 — Upper bound on s

There is no (46, 108, 823)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3089 560449 984016 698659 162067 574220 374285 528106 793751 130894 091183 553952 841189 > 5¹⁰⁸ [i]