MinT - Best Known (48−42, 48, s)-Nets in Base 9

Best Known (48−42, 48, s)-Nets in Base 9

(48−42, 48, 34)-Net over F₉ — Constructive and digital

Digital (6, 48, 34)-net over F₉, using

net from sequence [i] based on digital (6, 33)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
  - a function field by SÃ©mirat [i]

(48−42, 48, 35)-Net over F₉ — Digital

Digital (6, 48, 35)-net over F₉, using

net from sequence [i] based on digital (6, 34)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 35, using
  - Drinfeld modules of rank 1 [i]

(48−42, 48, 113)-Net in Base 9 — Upper bound on s

There is no (6, 48, 114)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁴⁸, 114, S₉, 42), but
- the linear programming bound shows that MÂ â‰¥ 178742 922548 708302 342120 089759 575955 416976 881295 942542 289756 659383 343611 785195 039633 / 26 770378 203904 826707 556512 572145 603142 > 9⁴⁸ [i]