MinT - Best Known (28, 28+96, s)-Nets in Base 5

Best Known (28, 28+96, s)-Nets in Base 5

(28, 28+96, 51)-Net over F₅ — Constructive and digital

Digital (28, 124, 51)-net over F₅, using

t-expansion [i] based on digital (22, 124, 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]

(28, 28+96, 55)-Net over F₅ — Digital

Digital (28, 124, 55)-net over F₅, using

t-expansion [i] based on digital (23, 124, 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]

(28, 28+96, 144)-Net in Base 5 — Upper bound on s

There is no (28, 124, 145)-net in base 5, because

1 times m-reduction [i] would yield (28, 123, 145)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5¹²³, 145, S₅, 95), but
  - the linear programming bound shows that MÂ â‰¥ 523946 922524 269524 545786 907827 294722 187715 168920 019132 326750 498085 399243 564097 560010 850429 534912 109375 / 4025 476446 595648 > 5¹²³ [i]