MinT - Best Known (29, 29+79, s)-Nets in Base 27

Best Known (29, 29+79, s)-Nets in Base 27

(29, 29+79, 114)-Net over F₂₇ — Constructive and digital

Digital (29, 108, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 108, 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]

(29, 29+79, 116)-Net in Base 27 — Constructive

(29, 108, 116)-net in base 27, using

base change [i] based on digital (2, 81, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(29, 29+79, 208)-Net over F₂₇ — Digital

Digital (29, 108, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 108, 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]

(29, 29+79, 4985)-Net in Base 27 — Upper bound on s

There is no (29, 108, 4986)-net in base 27, because

1 times m-reduction [i] would yield (29, 107, 4986)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1432 673902 243423 626001 475790 678289 583998 646411 655823 809987 897121 571470 362026 907309 137071 774514 660652 847952 571888 149506 495118 154154 423573 609544 260225 472953 > 27¹⁰⁷ [i]