MinT - Best Known (97−73, 97, s)-Nets in Base 27

Best Known (97−73, 97, s)-Nets in Base 27

(97−73, 97, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 97, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 97, 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]

(97−73, 97, 208)-Net over F₂₇ — Digital

Digital (24, 97, 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]

(97−73, 97, 3584)-Net in Base 27 — Upper bound on s

There is no (24, 97, 3585)-net in base 27, because

1 times m-reduction [i] would yield (24, 96, 3585)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 258322 263442 889821 174047 766521 238666 897439 388836 152535 820104 723172 583546 723840 650879 563022 183262 121539 958321 826565 854021 169083 851725 426545 > 27⁹⁶ [i]