MinT - Best Known (151−118, 151, s)-Nets in Base 8

Best Known (151−118, 151, s)-Nets in Base 8

(151−118, 151, 65)-Net over F₈ — Constructive and digital

Digital (33, 151, 65)-net over F₈, using

t-expansion [i] based on digital (14, 151, 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]

(151−118, 151, 97)-Net over F₈ — Digital

Digital (33, 151, 97)-net over F₈, using

t-expansion [i] based on digital (28, 151, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(151−118, 151, 630)-Net in Base 8 — Upper bound on s

There is no (33, 151, 631)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23615 382456 859961 836692 945501 097300 202379 450366 186323 726108 862303 075481 572996 209425 498079 274586 374248 408637 005453 661194 520638 435786 188640 > 8¹⁵¹ [i]