MinT - Best Known (153−105, 153, s)-Nets in Base 8

Best Known (153−105, 153, s)-Nets in Base 8

(153−105, 153, 98)-Net over F₈ — Constructive and digital

Digital (48, 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]

(153−105, 153, 144)-Net over F₈ — Digital

Digital (48, 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]

(153−105, 153, 1227)-Net in Base 8 — Upper bound on s

There is no (48, 153, 1228)-net in base 8, because

1 times m-reduction [i] would yield (48, 152, 1228)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186092 934469 574060 800295 353928 990658 096340 571996 964895 867149 614733 947807 106910 070553 886304 011044 782290 176126 247783 394023 215739 187025 606952 > 8¹⁵² [i]