MinT - Best Known (101−77, 101, s)-Nets in Base 27

Best Known (101−77, 101, s)-Nets in Base 27

(101−77, 101, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 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]

(101−77, 101, 208)-Net over F₂₇ — Digital

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]

(101−77, 101, 3357)-Net in Base 27 — Upper bound on s

There is no (24, 101, 3358)-net in base 27, because

1 times m-reduction [i] would yield (24, 100, 3358)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 137790 079862 917155 642949 125370 255965 272643 835985 813933 860528 852805 458268 297883 920160 701958 961159 219496 743836 526921 802517 678752 025158 318262 224229 > 27¹⁰⁰ [i]