MinT - Best Known (12, 12+22, s)-Nets in Base 7

Best Known (12, 12+22, s)-Nets in Base 7

(12, 12+22, 20)-Net over F₇ — Constructive and digital

Digital (12, 34, 20)-net over F₇, using

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

(12, 12+22, 38)-Net over F₇ — Digital

Digital (12, 34, 38)-net over F₇, using

t-expansion [i] based on digital (9, 34, 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+22, 328)-Net in Base 7 — Upper bound on s

There is no (12, 34, 329)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 55617 342561 268527 492837 915415 > 7³⁴ [i]