MinT - Best Known (155−109, 155, s)-Nets in Base 8

Best Known (155−109, 155, s)-Nets in Base 8

(155−109, 155, 98)-Net over F₈ — Constructive and digital

Digital (46, 155, 98)-net over F₈, using

t-expansion [i] based on digital (37, 155, 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]

(155−109, 155, 144)-Net over F₈ — Digital

Digital (46, 155, 144)-net over F₈, using

t-expansion [i] based on digital (45, 155, 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]

(155−109, 155, 1093)-Net in Base 8 — Upper bound on s

There is no (46, 155, 1094)-net in base 8, because

1 times m-reduction [i] would yield (46, 154, 1094)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12 435407 259170 515567 418339 720312 569840 421172 989650 459882 457066 077310 063793 886467 346524 165001 127988 093620 027115 560235 096298 711268 845197 453536 > 8¹⁵⁴ [i]