MinT - Best Known (27, 27+91, s)-Nets in Base 5

Best Known (27, 27+91, s)-Nets in Base 5

(27, 27+91, 51)-Net over F₅ — Constructive and digital

Digital (27, 118, 51)-net over F₅, using

t-expansion [i] based on digital (22, 118, 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, 27+91, 55)-Net over F₅ — Digital

Digital (27, 118, 55)-net over F₅, using

t-expansion [i] based on digital (23, 118, 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, 27+91, 141)-Net in Base 5 — Upper bound on s

There is no (27, 118, 142)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹¹⁸, 142, S₅, 91), but
- the linear programming bound shows that MÂ â‰¥ 227 290310 028755 622094 163273 225192 363202 339181 888847 417767 861303 072862 710905 610583 722591 400146 484375 / 5712 266942 976429 > 5¹¹⁸ [i]