MinT - Best Known (68, 68+63, s)-Nets in Base 9

Best Known (68, 68+63, s)-Nets in Base 9

(68, 68+63, 232)-Net over F₉ — Constructive and digital

Digital (68, 131, 232)-net over F₉, using

1 times m-reduction [i] based on digital (68, 132, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 66, 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]

(68, 68+63, 292)-Net over F₉ — Digital

Digital (68, 131, 292)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+63, 15562)-Net in Base 9 — Upper bound on s

There is no (68, 131, 15563)-net in base 9, because

1 times m-reduction [i] would yield (68, 130, 15563)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11271 278596 334172 193989 892747 037399 990459 444992 663564 863359 665550 849864 018668 153857 506342 102494 692152 924406 404927 720397 232425 > 9¹³⁰ [i]