MinT - Best Known (79−45, 79, s)-Nets in Base 7

Best Known (79−45, 79, s)-Nets in Base 7

(79−45, 79, 35)-Net over F₇ — Constructive and digital

Digital (34, 79, 35)-net over F₇, using

t-expansion [i] based on digital (33, 79, 35)-net over F₇, using
- net from sequence [i] based on digital (33, 34)-sequence over F₇, using
  - Niederreiter sequence [i]

(79−45, 79, 96)-Net over F₇ — Digital

Digital (34, 79, 96)-net over F₇, using

t-expansion [i] based on digital (33, 79, 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]

(79−45, 79, 1481)-Net in Base 7 — Upper bound on s

There is no (34, 79, 1482)-net in base 7, because

1 times m-reduction [i] would yield (34, 78, 1482)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 827644 564140 406546 375533 912353 200240 077318 797980 579450 670655 574429 > 7⁷⁸ [i]