MinT - Best Known (23, 23+76, s)-Nets in Base 5

Best Known (23, 23+76, s)-Nets in Base 5

(23, 23+76, 51)-Net over F₅ — Constructive and digital

Digital (23, 99, 51)-net over F₅, using

t-expansion [i] based on digital (22, 99, 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]

(23, 23+76, 55)-Net over F₅ — Digital

Digital (23, 99, 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]

(23, 23+76, 129)-Net in Base 5 — Upper bound on s

There is no (23, 99, 130)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁹⁹, 130, S₅, 76), but
- the linear programming bound shows that MÂ â‰¥ 2006 233802 346489 339335 710725 038384 645016 973676 177419 731616 984044 375584 517183 597199 618816 375732 421875 / 1 005715 779744 265762 696240 101539 > 5⁹⁹ [i]