MinT - Best Known (67, 67+61, s)-Nets in Base 9

Best Known (67, 67+61, s)-Nets in Base 9

(67, 67+61, 232)-Net over F₉ — Constructive and digital

Digital (67, 128, 232)-net over F₉, using

2 times m-reduction [i] based on digital (67, 130, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 65, 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]

(67, 67+61, 298)-Net over F₉ — Digital

Digital (67, 128, 298)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+61, 16475)-Net in Base 9 — Upper bound on s

There is no (67, 128, 16476)-net in base 9, because

1 times m-reduction [i] would yield (67, 127, 16476)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 452971 273271 511977 163208 257453 423678 803848 751774 810679 463090 053442 072773 378891 512165 121436 188999 456032 680603 414937 212609 > 9¹²⁷ [i]