MinT - Best Known (13, 42, s)-Nets in Base 128

Best Known (13, 42, s)-Nets in Base 128

(13, 42, 288)-Net over F₁₂₈ — Constructive and digital

Digital (13, 42, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 42, 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]

(13, 42, 321)-Net over F₁₂₈ — Digital

Digital (13, 42, 321)-net over F₁₂₈, using

t-expansion [i] based on digital (12, 42, 321)-net over F₁₂₈, using
- net from sequence [i] based on digital (12, 320)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 12 and N(F) ≥ 321, using
    - a curve from the manYPoints database [i]

(13, 42, 70587)-Net in Base 128 — Upper bound on s

There is no (13, 42, 70588)-net in base 128, because

1 times m-reduction [i] would yield (13, 41, 70588)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 248 682575 886138 764023 451051 366125 898018 431049 763280 828907 733880 263938 551042 999587 641508 > 128⁴¹ [i]