MinT - Best Known (59, 59+97, s)-Nets in Base 8

Best Known (59, 59+97, s)-Nets in Base 8

(59, 59+97, 98)-Net over F₈ — Constructive and digital

Digital (59, 156, 98)-net over F₈, using

t-expansion [i] based on digital (37, 156, 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]

(59, 59+97, 144)-Net over F₈ — Digital

Digital (59, 156, 144)-net over F₈, using

t-expansion [i] based on digital (45, 156, 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]

(59, 59+97, 2177)-Net in Base 8 — Upper bound on s

There is no (59, 156, 2178)-net in base 8, because

1 times m-reduction [i] would yield (59, 155, 2178)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 96 590292 784015 627568 504110 638935 484433 739212 583392 950372 270319 369399 092548 545262 057624 036016 670008 749056 340195 955766 265931 913644 661565 285192 > 8¹⁵⁵ [i]