MinT - Best Known (88−71, 88, s)-Nets in Base 27

Best Known (88−71, 88, s)-Nets in Base 27

(88−71, 88, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 88, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 88, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(88−71, 88, 144)-Net over F₂₇ — Digital

Digital (17, 88, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 88, 144)-net over F₂₇, using
- net from sequence [i] based on digital (16, 143)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 16 and N(F) ≥ 144, using
    - a curve from the manYPoints database [i]

(88−71, 88, 1914)-Net in Base 27 — Upper bound on s

There is no (17, 88, 1915)-net in base 27, because

1 times m-reduction [i] would yield (17, 87, 1915)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 33913 118377 996747 891381 756171 788685 366192 842840 266780 521705 557394 041059 623704 959214 285373 927505 193512 412703 066095 669901 472739 > 27⁸⁷ [i]