MinT - Best Known (103−77, 103, s)-Nets in Base 27

Best Known (103−77, 103, s)-Nets in Base 27

(103−77, 103, 114)-Net over F₂₇ — Constructive and digital

Digital (26, 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]

(103−77, 103, 208)-Net over F₂₇ — Digital

Digital (26, 103, 208)-net over F₂₇, using

t-expansion [i] based on 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]

(103−77, 103, 3997)-Net in Base 27 — Upper bound on s

There is no (26, 103, 3998)-net in base 27, because

1 times m-reduction [i] would yield (26, 102, 3998)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 100 599572 631070 133194 774219 867832 023833 194970 439777 770396 815104 156651 631387 712869 145978 210450 673523 350228 584477 271276 354505 768105 945402 789706 591333 > 27¹⁰² [i]