MinT - Best Known (60−47, 60, s)-Nets in Base 128

Best Known (60−47, 60, s)-Nets in Base 128

(60−47, 60, 288)-Net over F₁₂₈ — Constructive and digital

Digital (13, 60, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 60, 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]

(60−47, 60, 321)-Net over F₁₂₈ — Digital

Digital (13, 60, 321)-net over F₁₂₈, using

t-expansion [i] based on digital (12, 60, 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]

(60−47, 60, 18873)-Net in Base 128 — Upper bound on s

There is no (13, 60, 18874)-net in base 128, because

1 times m-reduction [i] would yield (13, 59, 18874)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 21172 737895 405811 278448 336309 305374 540334 599802 943516 737394 699591 552706 750094 128924 763035 921486 921836 689339 660744 467324 979580 > 128⁵⁹ [i]