MinT - Best Known (62, 62+56, s)-Nets in Base 9

Best Known (62, 62+56, s)-Nets in Base 9

(62, 62+56, 232)-Net over F₉ — Constructive and digital

Digital (62, 118, 232)-net over F₉, using

2 times m-reduction [i] based on digital (62, 120, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 60, 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]

(62, 62+56, 283)-Net over F₉ — Digital

Digital (62, 118, 283)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+56, 14820)-Net in Base 9 — Upper bound on s

There is no (62, 118, 14821)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39891 865544 833043 870341 015447 115534 026920 545772 173089 973324 347278 654375 989362 667647 265946 819056 339749 439119 008225 > 9¹¹⁸ [i]