MinT - Best Known (100−85, 100, s)-Nets in Base 27

Best Known (100−85, 100, s)-Nets in Base 27

(100−85, 100, 96)-Net over F₂₇ — Constructive and digital

Digital (15, 100, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 100, 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]

(100−85, 100, 136)-Net over F₂₇ — Digital

Digital (15, 100, 136)-net over F₂₇, using

t-expansion [i] based on digital (13, 100, 136)-net over F₂₇, using
- net from sequence [i] based on digital (13, 135)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 13 and N(F) ≥ 136, using
    - a curve from the manYPoints database [i]

(100−85, 100, 1480)-Net in Base 27 — Upper bound on s

There is no (15, 100, 1481)-net in base 27, because

1 times m-reduction [i] would yield (15, 99, 1481)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 5176 207879 394389 476810 006715 302691 859548 400966 328940 314867 160356 250858 959978 474319 808620 671352 844643 614787 344521 691052 410769 945970 708933 218825 > 27⁹⁹ [i]