MinT - Best Known (77−58, 77, s)-Nets in Base 128

Best Known (77−58, 77, s)-Nets in Base 128

(77−58, 77, 288)-Net over F₁₂₈ — Constructive and digital

Digital (19, 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]

(77−58, 77, 386)-Net over F₁₂₈ — Digital

Digital (19, 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]

(77−58, 77, 36153)-Net in Base 128 — Upper bound on s

There is no (19, 77, 36154)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 1 799942 209918 963612 621082 912455 813241 506862 630633 083459 226887 507389 219783 953009 292697 790368 155713 862767 306467 611393 279857 080895 848255 908410 708752 961158 495639 249320 > 128⁷⁷ [i]