MinT - Best Known (48, 48+87, s)-Nets in Base 9

Best Known (48, 48+87, s)-Nets in Base 9

(48, 48+87, 81)-Net over F₉ — Constructive and digital

Digital (48, 135, 81)-net over F₉, using

t-expansion [i] based on digital (32, 135, 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+87, 163)-Net over F₉ — Digital

Digital (48, 135, 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+87, 1960)-Net in Base 9 — Upper bound on s

There is no (48, 135, 1961)-net in base 9, because

1 times m-reduction [i] would yield (48, 134, 1961)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 75 300122 956598 415892 456742 397247 298582 885184 143140 544918 731243 488234 251361 106106 440176 224145 008668 848081 692935 278006 364461 502425 > 9¹³⁴ [i]