MinT - Best Known (27, 27+73, s)-Nets in Base 7

Best Known (27, 27+73, s)-Nets in Base 7

(27, 27+73, 32)-Net over F₇ — Constructive and digital

Digital (27, 100, 32)-net over F₇, using

net from sequence [i] based on digital (27, 31)-sequence over F₇, using
- Niederreiter sequence [i]

(27, 27+73, 78)-Net over F₇ — Digital

Digital (27, 100, 78)-net over F₇, using

net from sequence [i] based on digital (27, 77)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 27 and N(F) ≥ 78, using
  - an algebraic function field by Teo [i]

(27, 27+73, 478)-Net in Base 7 — Upper bound on s

There is no (27, 100, 479)-net in base 7, because

1 times m-reduction [i] would yield (27, 99, 479)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 471075 416601 880205 740711 148488 616788 095294 477276 081930 729874 183341 286658 774292 564265 > 7⁹⁹ [i]