MinT - Best Known (28, 28+81, s)-Nets in Base 27

Best Known (28, 28+81, s)-Nets in Base 27

(28, 28+81, 114)-Net over F₂₇ — Constructive and digital

Digital (28, 109, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 109, 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]

(28, 28+81, 208)-Net over F₂₇ — Digital

Digital (28, 109, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 109, 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]

(28, 28+81, 4420)-Net in Base 27 — Upper bound on s

There is no (28, 109, 4421)-net in base 27, because

1 times m-reduction [i] would yield (28, 108, 4421)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 38948 921162 984423 997930 906710 239964 047884 413140 563622 294550 762497 889076 449862 466455 359653 834412 612577 659251 390565 762652 231676 972930 159717 321488 085032 111393 > 27¹⁰⁸ [i]