MinT - Best Known (26, 80, s)-Nets in Base 5

Best Known (26, 80, s)-Nets in Base 5

(26, 80, 51)-Net over F₅ — Constructive and digital

Digital (26, 80, 51)-net over F₅, using

t-expansion [i] based on digital (22, 80, 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]

(26, 80, 55)-Net over F₅ — Digital

Digital (26, 80, 55)-net over F₅, using

t-expansion [i] based on digital (23, 80, 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]

(26, 80, 299)-Net in Base 5 — Upper bound on s

There is no (26, 80, 300)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁸⁰, 300, S₅, 54), but
- the linear programming bound shows that MÂ â‰¥ 2 266360 235068 117925 555056 572995 493733 438154 195362 577195 366043 921966 880108 148710 095838 152015 403466 066345 572471 618652 343750 000000 000000 / 24361 807139 976599 544379 615861 133207 382601 637670 258354 831434 446648 655831 977007 > 5⁸⁰ [i]