MinT - Best Known (29, 69, s)-Nets in Base 7

Best Known (29, 69, s)-Nets in Base 7

(29, 69, 33)-Net over F₇ — Constructive and digital

Digital (29, 69, 33)-net over F₇, using

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

(29, 69, 78)-Net over F₇ — Digital

Digital (29, 69, 78)-net over F₇, using

t-expansion [i] based on digital (27, 69, 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]

(29, 69, 1126)-Net in Base 7 — Upper bound on s

There is no (29, 69, 1127)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 20576 476857 784516 231351 183236 471673 884760 879332 175693 908361 > 7⁶⁹ [i]