MinT - Best Known (12, 12+35, s)-Nets in Base 7

Best Known (12, 12+35, s)-Nets in Base 7

(12, 12+35, 20)-Net over F₇ — Constructive and digital

Digital (12, 47, 20)-net over F₇, using

net from sequence [i] based on digital (12, 19)-sequence over F₇, using
- Niederreiter sequence [i]

(12, 12+35, 38)-Net over F₇ — Digital

Digital (12, 47, 38)-net over F₇, using

t-expansion [i] based on digital (9, 47, 38)-net over F₇, using
- net from sequence [i] based on digital (9, 37)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 9 and N(F) ≥ 38, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(12, 12+35, 220)-Net in Base 7 — Upper bound on s

There is no (12, 47, 221)-net in base 7, because

1 times m-reduction [i] would yield (12, 46, 221)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 759 113622 286088 900842 782944 093057 274799 > 7⁴⁶ [i]