MinT - Best Known (42, 42+46, s)-Nets in Base 8

Best Known (42, 42+46, s)-Nets in Base 8

(42, 42+46, 98)-Net over F₈ — Constructive and digital

Digital (42, 88, 98)-net over F₈, using

t-expansion [i] based on digital (37, 88, 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+46, 131)-Net over F₈ — Digital

Digital (42, 88, 131)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+46, 3828)-Net in Base 8 — Upper bound on s

There is no (42, 88, 3829)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 29 708395 249201 437493 579442 395297 765303 395726 208042 891213 330970 548386 659216 198880 > 8⁸⁸ [i]