MinT - Best Known (154−95, 154, s)-Nets in Base 8

Best Known (154−95, 154, s)-Nets in Base 8

(154−95, 154, 98)-Net over F₈ — Constructive and digital

Digital (59, 154, 98)-net over F₈, using

t-expansion [i] based on digital (37, 154, 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]

(154−95, 154, 144)-Net over F₈ — Digital

Digital (59, 154, 144)-net over F₈, using

t-expansion [i] based on digital (45, 154, 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]

(154−95, 154, 2255)-Net in Base 8 — Upper bound on s

There is no (59, 154, 2256)-net in base 8, because

1 times m-reduction [i] would yield (59, 153, 2256)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 513311 485492 630982 535408 352236 187821 350580 027221 289743 892669 352739 351675 368504 722187 899540 377250 542185 794811 729565 688819 399933 132859 197814 > 8¹⁵³ [i]