MinT - Best Known (12, 12+37, s)-Nets in Base 7

Best Known (12, 12+37, s)-Nets in Base 7

(12, 12+37, 20)-Net over F₇ — Constructive and digital

Digital (12, 49, 20)-net over F₇, using

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

(12, 12+37, 38)-Net over F₇ — Digital

Digital (12, 49, 38)-net over F₇, using

t-expansion [i] based on digital (9, 49, 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+37, 214)-Net in Base 7 — Upper bound on s

There is no (12, 49, 215)-net in base 7, because

1 times m-reduction [i] would yield (12, 48, 215)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 38472 796365 947463 448605 394194 110877 003013 > 7⁴⁸ [i]