MinT - Best Known (129−80, 129, s)-Nets in Base 8

Best Known (129−80, 129, s)-Nets in Base 8

(129−80, 129, 98)-Net over F₈ — Constructive and digital

Digital (49, 129, 98)-net over F₈, using

t-expansion [i] based on digital (37, 129, 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]

(129−80, 129, 144)-Net over F₈ — Digital

Digital (49, 129, 144)-net over F₈, using

t-expansion [i] based on digital (45, 129, 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]

(129−80, 129, 1816)-Net in Base 8 — Upper bound on s

There is no (49, 129, 1817)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 319 812238 297456 538139 658134 255688 536745 099096 191816 933775 218266 247003 184188 583887 004021 905514 811269 085593 934310 418440 > 8¹²⁹ [i]