MinT - Best Known (13, 13+59, s)-Nets in Base 128

Best Known (13, 13+59, s)-Nets in Base 128

(13, 13+59, 288)-Net over F₁₂₈ — Constructive and digital

Digital (13, 72, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 72, 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+59, 321)-Net over F₁₂₈ — Digital

Digital (13, 72, 321)-net over F₁₂₈, using

t-expansion [i] based on digital (12, 72, 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+59, 13239)-Net in Base 128 — Upper bound on s

There is no (13, 72, 13240)-net in base 128, because

1 times m-reduction [i] would yield (13, 71, 13240)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 409303 399689 254678 572150 225109 221704 798660 837634 961610 703652 722589 359197 279220 279507 127822 877704 316097 811208 801265 444043 116746 205709 101778 612897 974476 > 128⁷¹ [i]