MinT - Best Known (24, 24+83, s)-Nets in Base 5

Best Known (24, 24+83, s)-Nets in Base 5

(24, 24+83, 51)-Net over F₅ — Constructive and digital

Digital (24, 107, 51)-net over F₅, using

t-expansion [i] based on digital (22, 107, 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]

(24, 24+83, 55)-Net over F₅ — Digital

Digital (24, 107, 55)-net over F₅, using

t-expansion [i] based on digital (23, 107, 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]

(24, 24+83, 126)-Net in Base 5 — Upper bound on s

There is no (24, 107, 127)-net in base 5, because

1 times m-reduction [i] would yield (24, 106, 127)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5¹⁰⁶, 127, S₅, 82), but
  - the linear programming bound shows that MÂ â‰¥ 40 487096 187152 630316 758183 078765 316046 236804 017519 582410 411516 093518 002890 050411 224365 234375 / 319472 137902 581586 > 5¹⁰⁶ [i]