MinT - Best Known (28, 28+78, s)-Nets in Base 27

Best Known (28, 28+78, s)-Nets in Base 27

(28, 28+78, 114)-Net over F₂₇ — Constructive and digital

Digital (28, 106, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 106, 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+78, 208)-Net over F₂₇ — Digital

Digital (28, 106, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 106, 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+78, 4580)-Net in Base 27 — Upper bound on s

There is no (28, 106, 4581)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 53 380034 849722 481477 383398 344637 625829 670796 193351 051354 749282 803360 460817 315175 156819 372672 053262 782780 477027 317640 471531 456820 241438 592066 950987 748515 > 27¹⁰⁶ [i]