MinT - Best Known (12, 12+25, s)-Nets in Base 7

Best Known (12, 12+25, s)-Nets in Base 7

(12, 12+25, 20)-Net over F₇ — Constructive and digital

Digital (12, 37, 20)-net over F₇, using

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

(12, 12+25, 38)-Net over F₇ — Digital

Digital (12, 37, 38)-net over F₇, using

t-expansion [i] based on digital (9, 37, 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+25, 294)-Net in Base 7 — Upper bound on s

There is no (12, 37, 295)-net in base 7, because

1 times m-reduction [i] would yield (12, 36, 295)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2 661476 010243 087570 644943 573049 > 7³⁶ [i]