MinT - Best Known (99−82, 99, s)-Nets in Base 27

Best Known (99−82, 99, s)-Nets in Base 27

(99−82, 99, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 99, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 99, 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]

(99−82, 99, 144)-Net over F₂₇ — Digital

Digital (17, 99, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 99, 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]

(99−82, 99, 1753)-Net in Base 27 — Upper bound on s

There is no (17, 99, 1754)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 5150 134746 387360 697291 543645 185088 567593 173522 364300 250430 490973 433987 644861 153530 575459 893849 760468 358584 930927 935890 768442 712165 233974 695445 > 27⁹⁹ [i]