MinT - Best Known (139−103, 139, s)-Nets in Base 8

Best Known (139−103, 139, s)-Nets in Base 8

(139−103, 139, 65)-Net over F₈ — Constructive and digital

Digital (36, 139, 65)-net over F₈, using

t-expansion [i] based on digital (14, 139, 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]

(139−103, 139, 112)-Net over F₈ — Digital

Digital (36, 139, 112)-net over F₈, using

t-expansion [i] based on digital (35, 139, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(139−103, 139, 755)-Net in Base 8 — Upper bound on s

There is no (36, 139, 756)-net in base 8, because

1 times m-reduction [i] would yield (36, 138, 756)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42571 863433 145786 463964 641512 313861 136706 743762 523227 134582 188071 773242 622141 314444 244777 299967 567478 133109 082383 729630 651137 > 8¹³⁸ [i]