MinT - Best Known (48, 48+80, s)-Nets in Base 9

Best Known (48, 48+80, s)-Nets in Base 9

(48, 48+80, 81)-Net over F₉ — Constructive and digital

Digital (48, 128, 81)-net over F₉, using

t-expansion [i] based on digital (32, 128, 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+80, 163)-Net over F₉ — Digital

Digital (48, 128, 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+80, 2205)-Net in Base 9 — Upper bound on s

There is no (48, 128, 2206)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 140 420508 162568 460627 017220 639849 136041 058021 708000 136581 450354 688623 555650 769176 916560 409216 651774 901964 160150 874842 839169 > 9¹²⁸ [i]