MinT - Best Known (13, 13+49, s)-Nets in Base 128

Best Known (13, 13+49, s)-Nets in Base 128

(13, 13+49, 288)-Net over F₁₂₈ — Constructive and digital

Digital (13, 62, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 62, 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+49, 321)-Net over F₁₂₈ — Digital

Digital (13, 62, 321)-net over F₁₂₈, using

t-expansion [i] based on digital (12, 62, 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+49, 17502)-Net in Base 128 — Upper bound on s

There is no (13, 62, 17503)-net in base 128, because

1 times m-reduction [i] would yield (13, 61, 17503)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 346 929359 377272 031163 066446 679783 056347 132015 169250 429362 429426 004524 347891 661959 875357 579074 797686 172384 867449 796221 760939 154459 > 128⁶¹ [i]