MinT - Best Known (13, 13+65, s)-Nets in Base 128

Best Known (13, 13+65, s)-Nets in Base 128

(13, 13+65, 288)-Net over F₁₂₈ — Constructive and digital

Digital (13, 78, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 78, 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+65, 321)-Net over F₁₂₈ — Digital

Digital (13, 78, 321)-net over F₁₂₈, using

t-expansion [i] based on digital (12, 78, 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+65, 11829)-Net in Base 128 — Upper bound on s

There is no (13, 78, 11830)-net in base 128, because

1 times m-reduction [i] would yield (13, 77, 11830)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 1 801138 174121 755300 237557 607958 161415 577261 920154 709840 614056 415605 342982 445187 173343 652257 099493 108489 668111 009195 866578 806951 093717 442246 949651 810313 604566 500167 > 128⁷⁷ [i]