MinT - Best Known (121−93, 121, s)-Nets in Base 5

Best Known (121−93, 121, s)-Nets in Base 5

(121−93, 121, 51)-Net over F₅ — Constructive and digital

Digital (28, 121, 51)-net over F₅, using

t-expansion [i] based on digital (22, 121, 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]

(121−93, 121, 55)-Net over F₅ — Digital

Digital (28, 121, 55)-net over F₅, using

t-expansion [i] based on digital (23, 121, 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]

(121−93, 121, 147)-Net in Base 5 — Upper bound on s

There is no (28, 121, 148)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹²¹, 148, S₅, 93), but
- the linear programming bound shows that MÂ â‰¥ 32369 614861 849619 401750 006027 906460 896693 183159 168094 972472 912293 146030 116020 028799 539431 929588 317871 093750 / 5704 050953 652436 468413 > 5¹²¹ [i]