MinT - Best Known (42, 42+76, s)-Nets in Base 8

Best Known (42, 42+76, s)-Nets in Base 8

(42, 42+76, 98)-Net over F₈ — Constructive and digital

Digital (42, 118, 98)-net over F₈, using

t-expansion [i] based on digital (37, 118, 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, 42+76, 129)-Net over F₈ — Digital

Digital (42, 118, 129)-net over F₈, using

t-expansion [i] based on digital (38, 118, 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, 42+76, 1344)-Net in Base 8 — Upper bound on s

There is no (42, 118, 1345)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 37683 022163 026663 348016 630735 302773 490848 032829 859401 649917 760721 229797 533281 394925 579016 026762 352744 717408 > 8¹¹⁸ [i]