MinT - Best Known (81, 81+49, s)-Nets in Base 9

Best Known (81, 81+49, s)-Nets in Base 9

(81, 81+49, 740)-Net over F₉ — Constructive and digital

Digital (81, 130, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 65, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(81, 81+49, 924)-Net over F₉ — Digital

Digital (81, 130, 924)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+49, 164925)-Net in Base 9 — Upper bound on s

There is no (81, 130, 164926)-net in base 9, because

1 times m-reduction [i] would yield (81, 129, 164926)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1251 149928 814574 760700 164862 652131 437122 745532 684061 112680 474772 038807 742698 053398 442188 147555 749833 099482 661587 308543 054721 > 9¹²⁹ [i]