MinT - Best Known (115−89, 115, s)-Nets in Base 5

Best Known (115−89, 115, s)-Nets in Base 5

(115−89, 115, 51)-Net over F₅ — Constructive and digital

Digital (26, 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]

(115−89, 115, 55)-Net over F₅ — Digital

Digital (26, 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]

(115−89, 115, 135)-Net in Base 5 — Upper bound on s

There is no (26, 115, 136)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹¹⁵, 136, S₅, 89), but
- the linear programming bound shows that MÂ â‰¥ 270 602286 545732 863568 066789 328624 971103 435492 458442 156171 738446 346353 157423 436641 693115 234375 / 1 005178 694247 > 5¹¹⁵ [i]