MinT - Best Known (65, 65+106, s)-Nets in Base 8

Best Known (65, 65+106, s)-Nets in Base 8

(65, 65+106, 98)-Net over F₈ — Constructive and digital

Digital (65, 171, 98)-net over F₈, using

t-expansion [i] based on digital (37, 171, 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]

(65, 65+106, 144)-Net over F₈ — Digital

Digital (65, 171, 144)-net over F₈, using

t-expansion [i] based on digital (45, 171, 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]

(65, 65+106, 2378)-Net in Base 8 — Upper bound on s

There is no (65, 171, 2379)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 26876 757555 041714 639294 525597 142051 342614 077946 490278 532023 960254 604233 848334 385639 786468 931898 227824 527059 054092 077834 288565 413936 343764 038272 968951 317360 > 8¹⁷¹ [i]