MinT - Best Known (50, 50+92, s)-Nets in Base 8

Best Known (50, 50+92, s)-Nets in Base 8

(50, 50+92, 98)-Net over F₈ — Constructive and digital

Digital (50, 142, 98)-net over F₈, using

t-expansion [i] based on digital (37, 142, 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]

(50, 50+92, 144)-Net over F₈ — Digital

Digital (50, 142, 144)-net over F₈, using

t-expansion [i] based on digital (45, 142, 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]

(50, 50+92, 1548)-Net in Base 8 — Upper bound on s

There is no (50, 142, 1549)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 176 083825 538379 241344 160172 004905 782045 789158 499710 549151 976334 083534 858368 510437 021846 421502 943469 815856 553284 089339 623677 863680 > 8¹⁴² [i]