MinT - Best Known (13, 63, s)-Nets in Base 128

Best Known (13, 63, s)-Nets in Base 128

(13, 63, 288)-Net over F₁₂₈ — Constructive and digital

Digital (13, 63, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 63, 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, 63, 321)-Net over F₁₂₈ — Digital

Digital (13, 63, 321)-net over F₁₂₈, using

t-expansion [i] based on digital (12, 63, 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, 63, 16355)-Net in Base 128 — Upper bound on s

There is no (13, 63, 16356)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 5 681554 538014 729640 897416 504725 732033 601177 265212 209949 742534 667096 297843 373051 636153 826903 529002 051019 173449 397070 274599 493172 499796 > 128⁶³ [i]