MinT - Best Known (38, 38+39, s)-Nets in Base 8

Best Known (38, 38+39, s)-Nets in Base 8

(38, 38+39, 98)-Net over F₈ — Constructive and digital

Digital (38, 77, 98)-net over F₈, using

t-expansion [i] based on digital (37, 77, 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]

(38, 38+39, 135)-Net over F₈ — Digital

Digital (38, 77, 135)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+39, 4627)-Net in Base 8 — Upper bound on s

There is no (38, 77, 4628)-net in base 8, because

1 times m-reduction [i] would yield (38, 76, 4628)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 431 603756 836859 207785 988256 710573 631837 252627 962073 778183 202150 800383 > 8⁷⁶ [i]