MinT - Best Known (78, 78+71, s)-Nets in Base 9

Best Known (78, 78+71, s)-Nets in Base 9

(78, 78+71, 232)-Net over F₉ — Constructive and digital

Digital (78, 149, 232)-net over F₉, using

t-expansion [i] based on digital (77, 149, 232)-net over F₉, using
- 1 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]

(78, 78+71, 339)-Net over F₉ — Digital

Digital (78, 149, 339)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+71, 18826)-Net in Base 9 — Upper bound on s

There is no (78, 149, 18827)-net in base 9, because

1 times m-reduction [i] would yield (78, 148, 18827)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1692 380910 788297 389224 790741 138495 911911 605172 291807 496130 242972 703505 199112 158931 902739 321074 720091 024751 476441 025591 116252 395853 578105 369993 > 9¹⁴⁸ [i]