MinT - Best Known (103−79, 103, s)-Nets in Base 27

Best Known (103−79, 103, s)-Nets in Base 27

(103−79, 103, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 103, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 103, 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]

(103−79, 103, 208)-Net over F₂₇ — Digital

Digital (24, 103, 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]

(103−79, 103, 3260)-Net in Base 27 — Upper bound on s

There is no (24, 103, 3261)-net in base 27, because

1 times m-reduction [i] would yield (24, 102, 3261)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 100 242859 058474 599293 511345 607774 589888 484067 070599 393276 036501 946780 860390 522591 001653 976228 530732 550655 555073 032600 084083 577689 830027 938584 781251 > 27¹⁰² [i]