MinT - Best Known (135−103, 135, s)-Nets in Base 8

Best Known (135−103, 135, s)-Nets in Base 8

(135−103, 135, 65)-Net over F₈ — Constructive and digital

Digital (32, 135, 65)-net over F₈, using

t-expansion [i] based on digital (14, 135, 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]

(135−103, 135, 97)-Net over F₈ — Digital

Digital (32, 135, 97)-net over F₈, using

t-expansion [i] based on digital (28, 135, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(135−103, 135, 637)-Net in Base 8 — Upper bound on s

There is no (32, 135, 638)-net in base 8, because

1 times m-reduction [i] would yield (32, 134, 638)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 10 796994 088391 170870 643254 341791 583513 108574 618467 483344 961485 578750 736671 964718 239636 411883 910456 375343 993641 038577 211258 > 8¹³⁴ [i]