MinT - Best Known (113−94, 113, s)-Nets in Base 9

Best Known (113−94, 113, s)-Nets in Base 9

(113−94, 113, 74)-Net over F₉ — Constructive and digital

Digital (19, 113, 74)-net over F₉, using

t-expansion [i] based on digital (17, 113, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(113−94, 113, 84)-Net over F₉ — Digital

Digital (19, 113, 84)-net over F₉, using

net from sequence [i] based on digital (19, 83)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 19 and N(F) ≥ 84, using
  - Drinfeld modules of rank 1 [i]

(113−94, 113, 423)-Net in Base 9 — Upper bound on s

There is no (19, 113, 424)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 691530 031473 198102 562841 520522 882823 000633 361158 689970 012652 413104 663951 475305 812640 164636 801287 606210 802625 > 9¹¹³ [i]