MinT - Best Known (101−75, 101, s)-Nets in Base 27

Best Known (101−75, 101, s)-Nets in Base 27

(101−75, 101, 114)-Net over F₂₇ — Constructive and digital

Digital (26, 101, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 101, 114)-net over F₂₇, using
- net from sequence [i] based on digital (23, 113)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 23 and N(F) ≥ 114, using
    - an explicitly constructive algebraic function field [i]

(101−75, 101, 208)-Net over F₂₇ — Digital

Digital (26, 101, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 101, 208)-net over F₂₇, using
- net from sequence [i] based on digital (24, 207)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208, using
    - an algebraic function field by Beelen and Pellikaan [i]

(101−75, 101, 4144)-Net in Base 27 — Upper bound on s

There is no (26, 101, 4145)-net in base 27, because

1 times m-reduction [i] would yield (26, 100, 4145)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 137634 990652 478744 613302 727314 516605 072164 381682 521220 993990 549353 091852 930818 188366 093879 729433 757435 472569 465776 246011 497578 122633 157114 016203 > 27¹⁰⁰ [i]