MinT - Best Known (75, 75+65, s)-Nets in Base 9

Best Known (75, 75+65, s)-Nets in Base 9

(75, 75+65, 320)-Net over F₉ — Constructive and digital

Digital (75, 140, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 70, 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]

(75, 75+65, 359)-Net over F₉ — Digital

Digital (75, 140, 359)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+65, 22304)-Net in Base 9 — Upper bound on s

There is no (75, 140, 22305)-net in base 9, because

1 times m-reduction [i] would yield (75, 139, 22305)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 362349 027588 533486 598127 157186 666651 442544 232366 115331 194361 834034 669693 719834 808575 650168 580166 816954 019746 469191 907846 449979 399425 > 9¹³⁹ [i]