MinT - Best Known (153−109, 153, s)-Nets in Base 8

Best Known (153−109, 153, s)-Nets in Base 8

(153−109, 153, 98)-Net over F₈ — Constructive and digital

Digital (44, 153, 98)-net over F₈, using

t-expansion [i] based on digital (37, 153, 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]

(153−109, 153, 130)-Net over F₈ — Digital

Digital (44, 153, 130)-net over F₈, using

net from sequence [i] based on digital (44, 129)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 44 and N(F) ≥ 130, using
  - a curve from the manYPoints database [i]

(153−109, 153, 1009)-Net in Base 8 — Upper bound on s

There is no (44, 153, 1010)-net in base 8, because

1 times m-reduction [i] would yield (44, 152, 1010)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 190142 626751 390916 034910 444639 350841 515036 797172 667844 440899 850912 166451 235568 476611 174876 561239 614184 190999 412947 219206 699210 852029 143904 > 8¹⁵² [i]