MinT - Best Known (19, 19+49, s)-Nets in Base 7

Best Known (19, 19+49, s)-Nets in Base 7

(19, 19+49, 27)-Net over F₇ — Constructive and digital

Digital (19, 68, 27)-net over F₇, using

net from sequence [i] based on digital (19, 26)-sequence over F₇, using
- Niederreiter sequence [i]

(19, 19+49, 54)-Net over F₇ — Digital

Digital (19, 68, 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]

(19, 19+49, 358)-Net in Base 7 — Upper bound on s

There is no (19, 68, 359)-net in base 7, because

1 times m-reduction [i] would yield (19, 67, 359)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 436 611410 040332 010253 104978 900615 859302 959461 041670 118641 > 7⁶⁷ [i]