MinT - Best Known (37, 173, s)-Nets in Base 8

Best Known (37, 173, s)-Nets in Base 8

(37, 173, 98)-Net over F₈ — Constructive and digital

Digital (37, 173, 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]

(37, 173, 121)-Net over F₈ — Digital

Digital (37, 173, 121)-net over F₈, using

net from sequence [i] based on digital (37, 120)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 121, using
  - a curve from the manYPoints database [i]

(37, 173, 698)-Net in Base 8 — Upper bound on s

There is no (37, 173, 699)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 732270 639622 383820 501129 577271 074475 480401 265977 225178 869851 074458 924238 495093 001754 597147 815576 511571 043245 936879 866544 352213 737175 135872 884281 177125 465500 > 8¹⁷³ [i]