MinT - Best Known (17, 77, s)-Nets in Base 128

Best Known (17, 77, s)-Nets in Base 128

(17, 77, 288)-Net over F₁₂₈ — Constructive and digital

Digital (17, 77, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 77, 288)-net over F₁₂₈, using
- net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
    - a function field by SÃ©mirat [i]

(17, 77, 386)-Net over F₁₂₈ — Digital

Digital (17, 77, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 77, 386)-net over F₁₂₈, using
- net from sequence [i] based on digital (15, 385)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 15 and N(F) ≥ 386, using
    - a curve from the manYPoints database [i]

(17, 77, 24278)-Net in Base 128 — Upper bound on s

There is no (17, 77, 24279)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 1 800031 063569 570788 063452 910439 808171 472820 765906 574671 846995 829232 667480 816805 501971 174663 534087 029570 270053 018076 682727 507583 184296 882803 906361 364175 536021 061480 > 128⁷⁷ [i]