MinT - Best Known (156−113, 156, s)-Nets in Base 8

Best Known (156−113, 156, s)-Nets in Base 8

(156−113, 156, 98)-Net over F₈ — Constructive and digital

Digital (43, 156, 98)-net over F₈, using

t-expansion [i] based on digital (37, 156, 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]

(156−113, 156, 129)-Net over F₈ — Digital

Digital (43, 156, 129)-net over F₈, using

t-expansion [i] based on digital (38, 156, 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]

(156−113, 156, 944)-Net in Base 8 — Upper bound on s

There is no (43, 156, 945)-net in base 8, because

1 times m-reduction [i] would yield (43, 155, 945)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 96 641100 508852 500446 527128 831226 363275 299838 079321 062269 216487 186328 441842 870581 156250 953367 635428 329064 765322 815518 268263 346365 116669 535728 > 8¹⁵⁵ [i]