MinT - Best Known (100−77, 100, s)-Nets in Base 5

Best Known (100−77, 100, s)-Nets in Base 5

(100−77, 100, 51)-Net over F₅ — Constructive and digital

Digital (23, 100, 51)-net over F₅, using

t-expansion [i] based on digital (22, 100, 51)-net over F₅, using
- net from sequence [i] based on digital (22, 50)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
    - an explicitly constructive algebraic function field [i]

(100−77, 100, 55)-Net over F₅ — Digital

Digital (23, 100, 55)-net over F₅, using

net from sequence [i] based on digital (23, 54)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 23 and N(F) ≥ 55, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(100−77, 100, 125)-Net in Base 5 — Upper bound on s

There is no (23, 100, 126)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹⁰⁰, 126, S₅, 77), but
- the linear programming bound shows that MÂ â‰¥ 269 615872 401223 555455 941288 734660 705277 620669 322036 217607 774233 329109 847545 623779 296875 / 30952 288106 088453 > 5¹⁰⁰ [i]