MinT - Best Known (105−77, 105, s)-Nets in Base 27

Best Known (105−77, 105, s)-Nets in Base 27

(105−77, 105, 114)-Net over F₂₇ — Constructive and digital

Digital (28, 105, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 105, 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]

(105−77, 105, 208)-Net over F₂₇ — Digital

Digital (28, 105, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 105, 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]

(105−77, 105, 4758)-Net in Base 27 — Upper bound on s

There is no (28, 105, 4759)-net in base 27, because

1 times m-reduction [i] would yield (28, 104, 4759)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 73295 516950 200399 334631 638820 566673 534582 880433 531204 817994 144528 303679 110188 559883 992017 993639 356475 867434 246152 430346 894338 295986 288705 893897 973653 > 27¹⁰⁴ [i]