MinT - Best Known (145−79, 145, s)-Nets in Base 8

Best Known (145−79, 145, s)-Nets in Base 8

(145−79, 145, 113)-Net over F₈ — Constructive and digital

Digital (66, 145, 113)-net over F₈, using

3 times m-reduction [i] based on digital (66, 148, 113)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 52, 48)-net over F₈, using
    - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
        a function field by SÃ©mirat [i]
  2. digital (14, 96, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]

(145−79, 145, 168)-Net over F₈ — Digital

Digital (66, 145, 168)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−79, 145, 4726)-Net in Base 8 — Upper bound on s

There is no (66, 145, 4727)-net in base 8, because

1 times m-reduction [i] would yield (66, 144, 4727)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11111 015155 102789 394419 586772 141488 587746 115725 996151 145631 183565 866282 899716 563764 487464 439040 136730 080203 499014 711436 285652 193128 > 8¹⁴⁴ [i]