MinT - Best Known (20, 77, s)-Nets in Base 7

Best Known (20, 77, s)-Nets in Base 7

(20, 77, 28)-Net over F₇ — Constructive and digital

Digital (20, 77, 28)-net over F₇, using

net from sequence [i] based on digital (20, 27)-sequence over F₇, using
- Niederreiter sequence [i]

(20, 77, 54)-Net over F₇ — Digital

Digital (20, 77, 54)-net over F₇, using

t-expansion [i] based on digital (19, 77, 54)-net over F₇, using
- net from sequence [i] based on digital (19, 53)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 19 and N(F) ≥ 54, using
    - an algebraic function field by Teo [i]

(20, 77, 352)-Net in Base 7 — Upper bound on s

There is no (20, 77, 353)-net in base 7, because

1 times m-reduction [i] would yield (20, 76, 353)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 17492 068100 328450 500338 145713 267276 255409 773983 852164 252586 163873 > 7⁷⁶ [i]