MinT - Best Known (153−97, 153, s)-Nets in Base 8

Best Known (153−97, 153, s)-Nets in Base 8

(153−97, 153, 98)-Net over F₈ — Constructive and digital

Digital (56, 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]

(153−97, 153, 144)-Net over F₈ — Digital

Digital (56, 153, 144)-net over F₈, using

t-expansion [i] based on digital (45, 153, 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]

(153−97, 153, 1908)-Net in Base 8 — Upper bound on s

There is no (56, 153, 1909)-net in base 8, because

1 times m-reduction [i] would yield (56, 152, 1909)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 189159 745422 501981 340910 175509 743989 099401 038980 187211 509698 270102 975811 897253 264232 140626 660106 926296 053276 515284 928487 893805 696560 650975 > 8¹⁵² [i]