MinT - Best Known (28, 28+94, s)-Nets in Base 5

Best Known (28, 28+94, s)-Nets in Base 5

(28, 28+94, 51)-Net over F₅ — Constructive and digital

Digital (28, 122, 51)-net over F₅, using

t-expansion [i] based on digital (22, 122, 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+94, 55)-Net over F₅ — Digital

Digital (28, 122, 55)-net over F₅, using

t-expansion [i] based on digital (23, 122, 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+94, 145)-Net in Base 5 — Upper bound on s

There is no (28, 122, 146)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹²², 146, S₅, 94), but
- the linear programming bound shows that MÂ â‰¥ 211 795989 599382 257647 285884 795458 147343 177364 572503 310245 779281 108247 094067 564830 766059 458255 767822 265625 / 9 474927 760905 821721 > 5¹²² [i]