MinT - Best Known (131−76, 131, s)-Nets in Base 8

Best Known (131−76, 131, s)-Nets in Base 8

(131−76, 131, 98)-Net over F₈ — Constructive and digital

Digital (55, 131, 98)-net over F₈, using

t-expansion [i] based on digital (37, 131, 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]

(131−76, 131, 144)-Net over F₈ — Digital

Digital (55, 131, 144)-net over F₈, using

t-expansion [i] based on digital (45, 131, 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]

(131−76, 131, 2762)-Net in Base 8 — Upper bound on s

There is no (55, 131, 2763)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 20399 362396 632761 803594 305009 043474 993900 945354 027417 134657 977110 802251 295028 109855 747438 211153 107948 453935 424277 237476 > 8¹³¹ [i]