MinT - Best Known (48, 48+101, s)-Nets in Base 9

Best Known (48, 48+101, s)-Nets in Base 9

(48, 48+101, 81)-Net over F₉ — Constructive and digital

Digital (48, 149, 81)-net over F₉, using

t-expansion [i] based on digital (32, 149, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(48, 48+101, 163)-Net over F₉ — Digital

Digital (48, 149, 163)-net over F₉, using

net from sequence [i] based on digital (48, 162)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 48 and N(F) ≥ 163, using
  - Drinfeld modules of rank 1 [i]

(48, 48+101, 1595)-Net in Base 9 — Upper bound on s

There is no (48, 149, 1596)-net in base 9, because

1 times m-reduction [i] would yield (48, 148, 1596)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1718 755208 695393 244473 356111 952981 343930 262131 740483 855903 523494 558863 536295 779290 414747 065181 077471 368997 055307 681576 464847 312856 577765 077825 > 9¹⁴⁸ [i]