MinT - Best Known (42, 141, s)-Nets in Base 8

Best Known (42, 141, s)-Nets in Base 8

(42, 141, 98)-Net over F₈ — Constructive and digital

Digital (42, 141, 98)-net over F₈, using

t-expansion [i] based on digital (37, 141, 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]

(42, 141, 129)-Net over F₈ — Digital

Digital (42, 141, 129)-net over F₈, using

t-expansion [i] based on digital (38, 141, 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]

(42, 141, 1007)-Net in Base 8 — Upper bound on s

There is no (42, 141, 1008)-net in base 8, because

1 times m-reduction [i] would yield (42, 140, 1008)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 717527 705728 710732 222819 377596 305053 025164 832202 475860 875608 783321 938112 471033 291124 827154 570911 782572 325042 008161 054832 022684 > 8¹⁴⁰ [i]