MinT - Best Known (75, 75+71, s)-Nets in Base 9

Best Known (75, 75+71, s)-Nets in Base 9

(75, 75+71, 232)-Net over F₉ — Constructive and digital

Digital (75, 146, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 73, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(75, 75+71, 305)-Net over F₉ — Digital

Digital (75, 146, 305)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+71, 15590)-Net in Base 9 — Upper bound on s

There is no (75, 146, 15591)-net in base 9, because

1 times m-reduction [i] would yield (75, 145, 15591)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 319116 686421 103887 196633 370703 094202 565842 752311 390045 815866 523092 659469 340274 832909 289469 003459 010742 012335 326857 487089 656361 658735 826345 > 9¹⁴⁵ [i]