MinT - Best Known (145−99, 145, s)-Nets in Base 8

Best Known (145−99, 145, s)-Nets in Base 8

(145−99, 145, 98)-Net over F₈ — Constructive and digital

Digital (46, 145, 98)-net over F₈, using

t-expansion [i] based on digital (37, 145, 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]

(145−99, 145, 144)-Net over F₈ — Digital

Digital (46, 145, 144)-net over F₈, using

t-expansion [i] based on digital (45, 145, 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]

(145−99, 145, 1200)-Net in Base 8 — Upper bound on s

There is no (46, 145, 1201)-net in base 8, because

1 times m-reduction [i] would yield (46, 144, 1201)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11523 163561 665816 201250 744255 298274 645468 570596 052850 262051 719015 979185 914417 258078 460162 525395 957883 077158 822976 088420 470334 346664 > 8¹⁴⁴ [i]