MinT - Best Known (27, 27+51, s)-Nets in Base 7

Best Known (27, 27+51, s)-Nets in Base 7

(27, 27+51, 32)-Net over F₇ — Constructive and digital

Digital (27, 78, 32)-net over F₇, using

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

(27, 27+51, 78)-Net over F₇ — Digital

Digital (27, 78, 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+51, 663)-Net in Base 7 — Upper bound on s

There is no (27, 78, 664)-net in base 7, because

1 times m-reduction [i] would yield (27, 77, 664)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 119277 795416 925055 919117 384741 486024 880641 106611 730576 994637 874193 > 7⁷⁷ [i]