MinT - Best Known (15, 15+46, s)-Nets in Base 128

Best Known (15, 15+46, s)-Nets in Base 128

(15, 15+46, 288)-Net over F₁₂₈ — Constructive and digital

Digital (15, 61, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 61, 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]

(15, 15+46, 386)-Net over F₁₂₈ — Digital

Digital (15, 61, 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]

(15, 15+46, 28785)-Net in Base 128 — Upper bound on s

There is no (15, 61, 28786)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 346 769066 987320 799134 898618 494632 136927 249370 529782 717158 948440 205672 685821 683865 016215 556977 121488 541148 567954 338770 316838 877968 > 128⁶¹ [i]