MinT - Best Known (149−111, 149, s)-Nets in Base 8

Best Known (149−111, 149, s)-Nets in Base 8

(149−111, 149, 98)-Net over F₈ — Constructive and digital

Digital (38, 149, 98)-net over F₈, using

t-expansion [i] based on digital (37, 149, 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]

(149−111, 149, 129)-Net over F₈ — Digital

Digital (38, 149, 129)-net over F₈, using

net from sequence [i] based on digital (38, 128)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(149−111, 149, 786)-Net in Base 8 — Upper bound on s

There is no (38, 149, 787)-net in base 8, because

1 times m-reduction [i] would yield (38, 148, 787)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 47 610017 417104 822860 252552 371930 296173 997470 674303 286270 292507 226434 218050 578678 610764 102144 628554 429354 170051 266336 016264 290262 086912 > 8¹⁴⁸ [i]