MinT - Best Known (77−43, 77, s)-Nets in Base 7

Best Known (77−43, 77, s)-Nets in Base 7

(77−43, 77, 35)-Net over F₇ — Constructive and digital

Digital (34, 77, 35)-net over F₇, using

t-expansion [i] based on digital (33, 77, 35)-net over F₇, using
- net from sequence [i] based on digital (33, 34)-sequence over F₇, using
  - Niederreiter sequence [i]

(77−43, 77, 96)-Net over F₇ — Digital

Digital (34, 77, 96)-net over F₇, using

t-expansion [i] based on digital (33, 77, 96)-net over F₇, using
- net from sequence [i] based on digital (33, 95)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 33 and N(F) ≥ 96, using
    - an algebraic function field by Teo [i]

(77−43, 77, 1641)-Net in Base 7 — Upper bound on s

There is no (34, 77, 1642)-net in base 7, because

1 times m-reduction [i] would yield (34, 76, 1642)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 16988 264956 221961 661280 372999 315091 085007 888790 462917 129816 221461 > 7⁷⁶ [i]