MinT - Best Known (76−59, 76, s)-Nets in Base 8

Best Known (76−59, 76, s)-Nets in Base 8

(76−59, 76, 65)-Net over F₈ — Constructive and digital

Digital (17, 76, 65)-net over F₈, using

t-expansion [i] based on digital (14, 76, 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]

(76−59, 76, 343)-Net in Base 8 — Upper bound on s

There is no (17, 76, 344)-net in base 8, because

1 times m-reduction [i] would yield (17, 75, 344)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 57 448601 486562 778314 988230 541819 816444 307226 077458 015628 532934 182472 > 8⁷⁵ [i]