MinT - Best Known (76−51, 76, s)-Nets in Base 5

Best Known (76−51, 76, s)-Nets in Base 5

(76−51, 76, 51)-Net over F₅ — Constructive and digital

Digital (25, 76, 51)-net over F₅, using

t-expansion [i] based on digital (22, 76, 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]

(76−51, 76, 55)-Net over F₅ — Digital

Digital (25, 76, 55)-net over F₅, using

t-expansion [i] based on digital (23, 76, 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]

(76−51, 76, 299)-Net in Base 5 — Upper bound on s

There is no (25, 76, 300)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁷⁶, 300, S₅, 51), but
- the linear programming bound shows that MÂ â‰¥ 237 093698 815934 923988 017019 139393 100344 855851 776989 247815 621981 025377 616810 146719 217300 415039 062500 000000 000000 000000 / 1654 484829 899024 668832 595818 748726 582640 089399 871965 785049 707797 > 5⁷⁶ [i]