MinT - Best Known (77−56, 77, s)-Nets in Base 128

Best Known (77−56, 77, s)-Nets in Base 128

(77−56, 77, 288)-Net over F₁₂₈ — Constructive and digital

Digital (21, 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]

(77−56, 77, 386)-Net over F₁₂₈ — Digital

Digital (21, 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]

(77−56, 77, 55452)-Net in Base 128 — Upper bound on s

There is no (21, 77, 55453)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 1 800001 646440 631282 485220 278709 269329 588182 806143 621163 908892 953147 641183 243768 373723 970541 060089 182891 314350 980600 918098 497731 964061 272327 206068 178520 059499 079049 > 128⁷⁷ [i]