MinT - Best Known (128−78, 128, s)-Nets in Base 8

Best Known (128−78, 128, s)-Nets in Base 8

(128−78, 128, 98)-Net over F₈ — Constructive and digital

Digital (50, 128, 98)-net over F₈, using

t-expansion [i] based on digital (37, 128, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(128−78, 128, 144)-Net over F₈ — Digital

Digital (50, 128, 144)-net over F₈, using

t-expansion [i] based on digital (45, 128, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(128−78, 128, 2000)-Net in Base 8 — Upper bound on s

There is no (50, 128, 2001)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 40 163945 587328 433093 060773 254797 094989 570037 482950 423084 059664 172579 618196 495677 399579 699808 020133 779501 892590 750112 > 8¹²⁸ [i]