MinT - Best Known (11, 11+61, s)-Nets in Base 128

Best Known (11, 11+61, s)-Nets in Base 128

(11, 11+61, 288)-Net over F₁₂₈ — Constructive and digital

Digital (11, 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]

(11, 11+61, 296)-Net over F₁₂₈ — Digital

Digital (11, 72, 296)-net over F₁₂₈, using

t-expansion [i] based on digital (10, 72, 296)-net over F₁₂₈, using
- net from sequence [i] based on digital (10, 295)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 10 and N(F) ≥ 296, using
    - a curve from the manYPoints database [i]

(11, 11+61, 321)-Net in Base 128

(11, 72, 321)-net in base 128, using

base change [i] based on digital (2, 63, 321)-net over F₂₅₆, using
- net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
    - sharp bound on the number of rational points on curves with genus 2 [i]

(11, 11+61, 9190)-Net in Base 128 — Upper bound on s

There is no (11, 72, 9191)-net in base 128, because

1 times m-reduction [i] would yield (11, 71, 9191)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 409450 174815 681207 195877 055575 597130 391267 047231 188143 005776 765287 043994 516562 071551 157892 995952 496853 738105 760289 288497 797910 599054 617115 846997 827628 > 128⁷¹ [i]