MinT - Best Known (146−98, 146, s)-Nets in Base 9

Best Known (146−98, 146, s)-Nets in Base 9

(146−98, 146, 81)-Net over F₉ — Constructive and digital

Digital (48, 146, 81)-net over F₉, using

t-expansion [i] based on digital (32, 146, 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]

(146−98, 146, 163)-Net over F₉ — Digital

Digital (48, 146, 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]

(146−98, 146, 1635)-Net in Base 9 — Upper bound on s

There is no (48, 146, 1636)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21 328287 823558 280543 231539 080333 210488 747992 364863 681571 524614 794826 243194 397844 701608 810847 787010 853931 694475 757706 898792 694044 329263 293729 > 9¹⁴⁶ [i]