MinT - Best Known (136−109, 136, s)-Nets in Base 8

Best Known (136−109, 136, s)-Nets in Base 8

(136−109, 136, 65)-Net over F₈ — Constructive and digital

Digital (27, 136, 65)-net over F₈, using

t-expansion [i] based on digital (14, 136, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(136−109, 136, 96)-Net over F₈ — Digital

Digital (27, 136, 96)-net over F₈, using

net from sequence [i] based on digital (27, 95)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 27 and N(F) ≥ 96, using
  - a curve from the manYPoints database [i]

(136−109, 136, 508)-Net in Base 8 — Upper bound on s

There is no (27, 136, 509)-net in base 8, because

1 times m-reduction [i] would yield (27, 135, 509)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 85 678581 011516 204278 920406 462901 702211 231288 926393 219216 913711 092978 585633 508241 824040 927151 369162 619896 800504 251595 452172 > 8¹³⁵ [i]