MinT - Best Known (56, 151, s)-Nets in Base 8

Best Known (56, 151, s)-Nets in Base 8

(56, 151, 98)-Net over F₈ — Constructive and digital

Digital (56, 151, 98)-net over F₈, using

t-expansion [i] based on digital (37, 151, 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]

(56, 151, 144)-Net over F₈ — Digital

Digital (56, 151, 144)-net over F₈, using

t-expansion [i] based on digital (45, 151, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(56, 151, 1971)-Net in Base 8 — Upper bound on s

There is no (56, 151, 1972)-net in base 8, because

1 times m-reduction [i] would yield (56, 150, 1972)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2961 277876 829895 640550 257911 735754 226165 978135 560024 890965 611130 759933 830610 630008 228111 932474 829363 401090 442063 424158 624870 288457 869764 > 8¹⁵⁰ [i]