MinT - Best Known (77, 77+73, s)-Nets in Base 9

Best Known (77, 77+73, s)-Nets in Base 9

(77, 77+73, 232)-Net over F₉ — Constructive and digital

Digital (77, 150, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 75, 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]

(77, 77+73, 311)-Net over F₉ — Digital

Digital (77, 150, 311)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+73, 15868)-Net in Base 9 — Upper bound on s

There is no (77, 150, 15869)-net in base 9, because

1 times m-reduction [i] would yield (77, 149, 15869)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15210 369249 246715 865687 131336 942471 905314 426298 875810 081176 104939 101522 386833 289886 832464 271777 505790 685101 587184 323693 334094 685046 320825 322785 > 9¹⁴⁹ [i]