MinT - Best Known (161−123, 161, s)-Nets in Base 8

Best Known (161−123, 161, s)-Nets in Base 8

(161−123, 161, 98)-Net over F₈ — Constructive and digital

Digital (38, 161, 98)-net over F₈, using

t-expansion [i] based on digital (37, 161, 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]

(161−123, 161, 129)-Net over F₈ — Digital

Digital (38, 161, 129)-net over F₈, using

net from sequence [i] based on digital (38, 128)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(161−123, 161, 748)-Net in Base 8 — Upper bound on s

There is no (38, 161, 749)-net in base 8, because

1 times m-reduction [i] would yield (38, 160, 749)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 198643 640292 973245 502272 578050 590789 716558 343157 133053 601929 851052 709870 480200 801712 098244 939097 846895 633195 058086 479784 249397 993876 975679 613344 > 8¹⁶⁰ [i]