MinT - Best Known (49, 49+97, s)-Nets in Base 9

Best Known (49, 49+97, s)-Nets in Base 9

(49, 49+97, 81)-Net over F₉ — Constructive and digital

Digital (49, 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]

(49, 49+97, 168)-Net over F₉ — Digital

Digital (49, 146, 168)-net over F₉, using

net from sequence [i] based on digital (49, 167)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 49 and N(F) ≥ 168, using
  - Drinfeld modules of rank 1 [i]

(49, 49+97, 1758)-Net in Base 9 — Upper bound on s

There is no (49, 146, 1759)-net in base 9, because

1 times m-reduction [i] would yield (49, 145, 1759)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 356305 120803 526525 718219 308853 621502 188496 117877 514806 010695 121694 763421 793526 524045 308211 986659 547697 403659 029167 734071 520981 645349 416577 > 9¹⁴⁵ [i]