MinT - Best Known (10, 10+67, s)-Nets in Base 9

Best Known (10, 10+67, s)-Nets in Base 9

(10, 10+67, 40)-Net over F₉ — Constructive and digital

Digital (10, 77, 40)-net over F₉, using

t-expansion [i] based on digital (8, 77, 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+67, 54)-Net over F₉ — Digital

Digital (10, 77, 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+67, 140)-Net in Base 9 — Upper bound on s

There is no (10, 77, 141)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁷⁷, 141, S₉, 67), but
- the linear programming bound shows that MÂ â‰¥ 22 695884 346341 824397 310481 039109 690822 078166 603798 762196 090278 862561 150501 913731 910681 470091 908466 064985 061652 705588 317801 560602 615565 719624 351779 364930 030169 895313 / 725032 893276 354923 141686 602115 507383 543485 091908 836983 691699 295011 594455 893033 079364 019993 > 9⁷⁷ [i]