MinT - Best Known (135−80, 135, s)-Nets in Base 8

Best Known (135−80, 135, s)-Nets in Base 8

(135−80, 135, 98)-Net over F₈ — Constructive and digital

Digital (55, 135, 98)-net over F₈, using

t-expansion [i] based on digital (37, 135, 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]

(135−80, 135, 144)-Net over F₈ — Digital

Digital (55, 135, 144)-net over F₈, using

t-expansion [i] based on digital (45, 135, 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]

(135−80, 135, 2490)-Net in Base 8 — Upper bound on s

There is no (55, 135, 2491)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 83 493272 258339 713363 965108 093402 942621 343308 305948 209054 097171 287030 937498 282848 160175 928599 497083 165296 440972 548770 334105 > 8¹³⁵ [i]