MinT - Best Known (10, 10+71, s)-Nets in Base 9

Best Known (10, 10+71, s)-Nets in Base 9

(10, 10+71, 40)-Net over F₉ — Constructive and digital

Digital (10, 81, 40)-net over F₉, using

t-expansion [i] based on digital (8, 81, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(10, 10+71, 54)-Net over F₉ — Digital

Digital (10, 81, 54)-net over F₉, using

net from sequence [i] based on digital (10, 53)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 10 and N(F) ≥ 54, using
  - a curve from the manYPoints database [i]

(10, 10+71, 118)-Net in Base 9 — Upper bound on s

There is no (10, 81, 119)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁸¹, 119, S₉, 71), but
- the linear programming bound shows that MÂ â‰¥ 214708 069385 240374 484670 841358 600054 512946 959810 883622 937885 230227 950868 856352 683234 456776 183501 428762 053456 000009 / 1 052647 913468 527687 002299 308596 320425 > 9⁸¹ [i]