MinT - Best Known (42, 42+113, s)-Nets in Base 8

Best Known (42, 42+113, s)-Nets in Base 8

(42, 42+113, 98)-Net over F₈ — Constructive and digital

Digital (42, 155, 98)-net over F₈, using

t-expansion [i] based on digital (37, 155, 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+113, 129)-Net over F₈ — Digital

Digital (42, 155, 129)-net over F₈, using

t-expansion [i] based on digital (38, 155, 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+113, 909)-Net in Base 8 — Upper bound on s

There is no (42, 155, 910)-net in base 8, because

1 times m-reduction [i] would yield (42, 154, 910)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12 601700 480446 961602 800837 176404 759934 977778 049335 160982 268067 273949 140563 073702 064513 150242 521785 767303 399277 015063 286893 285452 314745 623800 > 8¹⁵⁴ [i]