MinT - Best Known (95−71, 95, s)-Nets in Base 27

Best Known (95−71, 95, s)-Nets in Base 27

(95−71, 95, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 95, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 95, 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]

(95−71, 95, 208)-Net over F₂₇ — Digital

Digital (24, 95, 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]

(95−71, 95, 3718)-Net in Base 27 — Upper bound on s

There is no (24, 95, 3719)-net in base 27, because

1 times m-reduction [i] would yield (24, 94, 3719)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 354 380319 332951 855067 608645 708718 934311 034686 985573 343592 114260 640454 057314 246536 138308 852733 194999 799072 232197 115720 072415 720125 235155 > 27⁹⁴ [i]