MinT - Best Known (16, 16+108, s)-Nets in Base 9

Best Known (16, 16+108, s)-Nets in Base 9

(16, 16+108, 64)-Net over F₉ — Constructive and digital

Digital (16, 124, 64)-net over F₉, using

t-expansion [i] based on digital (13, 124, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(16, 16+108, 74)-Net over F₉ — Digital

Digital (16, 124, 74)-net over F₉, using

net from sequence [i] based on digital (16, 73)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 16 and N(F) ≥ 74, using
  - a curve from the manYPoints database [i]

(16, 16+108, 148)-Net in Base 9 — Upper bound on s

There is no (16, 124, 149)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9¹²⁴, 149, S₉, 108), but
- the linear programming bound shows that MÂ â‰¥ 129 762098 268906 792150 740869 214915 365077 702077 949600 817737 085039 490763 810846 464289 848466 614529 516496 531631 901557 699842 053674 080542 262398 898269 / 4065 724117 534876 671875 > 9¹²⁴ [i]