MinT - Best Known (79−50, 79, s)-Nets in Base 7

Best Known (79−50, 79, s)-Nets in Base 7

(79−50, 79, 33)-Net over F₇ — Constructive and digital

Digital (29, 79, 33)-net over F₇, using

net from sequence [i] based on digital (29, 32)-sequence over F₇, using
- Niederreiter sequence [i]

(79−50, 79, 78)-Net over F₇ — Digital

Digital (29, 79, 78)-net over F₇, using

t-expansion [i] based on digital (27, 79, 78)-net over F₇, using
- net from sequence [i] based on digital (27, 77)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 27 and N(F) ≥ 78, using
    - an algebraic function field by Teo [i]

(79−50, 79, 778)-Net in Base 7 — Upper bound on s

There is no (29, 79, 779)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 5 931355 767006 735266 001434 746056 500714 268860 322916 024951 779810 229363 > 7⁷⁹ [i]