MinT - Best Known (102−75, 102, s)-Nets in Base 27

Best Known (102−75, 102, s)-Nets in Base 27

(102−75, 102, 114)-Net over F₂₇ — Constructive and digital

Digital (27, 102, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 102, 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]

(102−75, 102, 208)-Net over F₂₇ — Digital

Digital (27, 102, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 102, 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]

(102−75, 102, 4532)-Net in Base 27 — Upper bound on s

There is no (27, 102, 4533)-net in base 27, because

1 times m-reduction [i] would yield (27, 101, 4533)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 3 716969 834516 113826 022858 857640 794462 799928 262037 241426 639543 775790 954720 091391 026410 732987 473350 676231 037843 264841 569018 977226 832323 628092 790867 > 27¹⁰¹ [i]