MinT - Best Known (104−79, 104, s)-Nets in Base 27

Best Known (104−79, 104, s)-Nets in Base 27

(104−79, 104, 114)-Net over F₂₇ — Constructive and digital

Digital (25, 104, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 104, 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]

(104−79, 104, 208)-Net over F₂₇ — Digital

Digital (25, 104, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 104, 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]

(104−79, 104, 3549)-Net in Base 27 — Upper bound on s

There is no (25, 104, 3550)-net in base 27, because

1 times m-reduction [i] would yield (25, 103, 3550)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 2695 781148 974010 271787 766644 359120 548210 179684 752619 990836 610326 110377 714359 378553 800164 635738 200145 894744 825410 128235 898121 969442 928682 598653 980233 > 27¹⁰³ [i]