MinT - Best Known (66, 66+56, s)-Nets in Base 9

Best Known (66, 66+56, s)-Nets in Base 9

(66, 66+56, 320)-Net over F₉ — Constructive and digital

Digital (66, 122, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 61, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(66, 66+56, 336)-Net over F₉ — Digital

Digital (66, 122, 336)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+56, 20291)-Net in Base 9 — Upper bound on s

There is no (66, 122, 20292)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 261 610634 371933 168920 490392 721750 144339 927657 590807 283457 508883 288624 064203 666748 707843 304111 385622 263664 401785 818241 > 9¹²² [i]