MinT - Best Known (27, 119, s)-Nets in Base 5

Best Known (27, 119, s)-Nets in Base 5

(27, 119, 51)-Net over F₅ — Constructive and digital

Digital (27, 119, 51)-net over F₅, using

t-expansion [i] based on digital (22, 119, 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]

(27, 119, 55)-Net over F₅ — Digital

Digital (27, 119, 55)-net over F₅, using

t-expansion [i] based on digital (23, 119, 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]

(27, 119, 140)-Net in Base 5 — Upper bound on s

There is no (27, 119, 141)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹¹⁹, 141, S₅, 92), but
- the linear programming bound shows that MÂ â‰¥ 11975 432670 441004 977539 635219 646164 313897 650335 989689 639442 506985 389513 829431 962221 860885 620117 187500 / 54190 349279 215097 > 5¹¹⁹ [i]