MinT - Best Known (99−75, 99, s)-Nets in Base 5

Best Known (99−75, 99, s)-Nets in Base 5

(99−75, 99, 51)-Net over F₅ — Constructive and digital

Digital (24, 99, 51)-net over F₅, using

t-expansion [i] based on digital (22, 99, 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]

(99−75, 99, 55)-Net over F₅ — Digital

Digital (24, 99, 55)-net over F₅, using

t-expansion [i] based on digital (23, 99, 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]

(99−75, 99, 146)-Net in Base 5 — Upper bound on s

There is no (24, 99, 147)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁹⁹, 147, S₅, 75), but
- the linear programming bound shows that MÂ â‰¥ 10 465163 072971 841494 226679 044239 098519 996159 375872 949750 717770 995481 826038 130942 490580 153891 865933 246663 189493 119716 644287 109375 / 6623 020670 394833 160024 516013 529216 797975 034523 571498 254336 > 5⁹⁹ [i]