MinT - Best Known (133−119, 133, s)-Nets in Base 9

Best Known (133−119, 133, s)-Nets in Base 9

(133−119, 133, 64)-Net over F₉ — Constructive and digital

Digital (14, 133, 64)-net over F₉, using

t-expansion [i] based on digital (13, 133, 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]

(133−119, 133, 127)-Net in Base 9 — Upper bound on s

There is no (14, 133, 128)-net in base 9, because

18 times m-reduction [i] would yield (14, 115, 128)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9¹¹⁵, 128, S₉, 101), but
  - the linear programming bound shows that MÂ â‰¥ 443 166910 356198 778018 116730 424202 752086 605368 053990 969284 924273 837502 116929 265381 334877 312358 520249 430979 777899 498996 052429 / 7 631616 168397 > 9¹¹⁵ [i]