MinT - Best Known (27, 115, s)-Nets in Base 5

Best Known (27, 115, s)-Nets in Base 5

(27, 115, 51)-Net over F₅ — Constructive and digital

Digital (27, 115, 51)-net over F₅, using

t-expansion [i] based on digital (22, 115, 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, 115, 55)-Net over F₅ — Digital

Digital (27, 115, 55)-net over F₅, using

t-expansion [i] based on digital (23, 115, 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, 115, 146)-Net in Base 5 — Upper bound on s

There is no (27, 115, 147)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹¹⁵, 147, S₅, 88), but
- the linear programming bound shows that MÂ â‰¥ 2106 427198 388426 824206 051416 107971 920370 889275 492662 277335 854828 334837 929304 512726 957909 762859 344482 421875 / 6 144065 730517 820384 976983 > 5¹¹⁵ [i]