MinT - Best Known (16, 16+87, s)-Nets in Base 27

Best Known (16, 16+87, s)-Nets in Base 27

(16, 16+87, 96)-Net over F₂₇ — Constructive and digital

Digital (16, 103, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 103, 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]

(16, 16+87, 144)-Net over F₂₇ — Digital

Digital (16, 103, 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]

(16, 16+87, 1591)-Net in Base 27 — Upper bound on s

There is no (16, 103, 1592)-net in base 27, because

1 times m-reduction [i] would yield (16, 102, 1592)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 102 168077 534947 688928 577826 037447 919209 033355 801085 617763 451679 045719 234286 430328 447171 972581 692666 172577 525021 520791 737645 486523 702078 690263 339425 > 27¹⁰² [i]