MinT - Best Known (13, 13+56, s)-Nets in Base 128

Best Known (13, 13+56, s)-Nets in Base 128

(13, 13+56, 288)-Net over F₁₂₈ — Constructive and digital

Digital (13, 69, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 69, 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, 13+56, 321)-Net over F₁₂₈ — Digital

Digital (13, 69, 321)-net over F₁₂₈, using

t-expansion [i] based on digital (12, 69, 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, 13+56, 13852)-Net in Base 128 — Upper bound on s

There is no (13, 69, 13853)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 24 981954 983161 822242 087897 463108 520195 499050 436128 462403 431224 298640 206349 591532 211521 370213 363399 102923 702940 371965 723878 059543 342208 822422 847841 > 128⁶⁹ [i]