MinT - Best Known (27, 27+87, s)-Nets in Base 5

Best Known (27, 27+87, s)-Nets in Base 5

(27, 27+87, 51)-Net over F₅ — Constructive and digital

Digital (27, 114, 51)-net over F₅, using

t-expansion [i] based on digital (22, 114, 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+87, 55)-Net over F₅ — Digital

Digital (27, 114, 55)-net over F₅, using

t-expansion [i] based on digital (23, 114, 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+87, 147)-Net in Base 5 — Upper bound on s

There is no (27, 114, 148)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹¹⁴, 148, S₅, 87), but
- the linear programming bound shows that MÂ â‰¥ 63687 687420 768027 997189 489566 120495 525254 388256 273970 899556 895034 800130 250829 397482 448257 505893 707275 390625 / 1273 099402 224877 219656 507008 > 5¹¹⁴ [i]