MinT - Best Known (77, 77+71, s)-Nets in Base 9

Best Known (77, 77+71, s)-Nets in Base 9

(77, 77+71, 232)-Net over F₉ — Constructive and digital

Digital (77, 148, 232)-net over F₉, using

2 times m-reduction [i] based on 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+71, 328)-Net over F₉ — Digital

Digital (77, 148, 328)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+71, 17679)-Net in Base 9 — Upper bound on s

There is no (77, 148, 17680)-net in base 9, because

1 times m-reduction [i] would yield (77, 147, 17680)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 187 998964 890132 463971 630712 392068 855672 272238 223006 608495 669259 425966 511020 272191 434888 244915 181134 386365 921261 023349 024131 741995 998260 416385 > 9¹⁴⁷ [i]