MinT - Best Known (99−73, 99, s)-Nets in Base 27

Best Known (99−73, 99, s)-Nets in Base 27

(99−73, 99, 114)-Net over F₂₇ — Constructive and digital

Digital (26, 99, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 99, 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]

(99−73, 99, 208)-Net over F₂₇ — Digital

Digital (26, 99, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 99, 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]

(99−73, 99, 4308)-Net in Base 27 — Upper bound on s

There is no (26, 99, 4309)-net in base 27, because

1 times m-reduction [i] would yield (26, 98, 4309)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 188 089106 910740 029919 793491 158246 951569 382057 619553 966073 375208 522862 039738 601581 369205 000541 085096 260926 640416 249008 400545 062780 498628 234225 > 27⁹⁸ [i]