MinT - Best Known (73−59, 73, s)-Nets in Base 81

Best Known (73−59, 73, s)-Nets in Base 81

(73−59, 73, 224)-Net over F₈₁ — Constructive and digital

Digital (14, 73, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 73, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(73−59, 73, 298)-Net over F₈₁ — Digital

Digital (14, 73, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 73, 298)-net over F₈₁, using
- net from sequence [i] based on digital (12, 297)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 12 and N(F) ≥ 298, using
    - a curve from the manYPoints database [i]

(73−59, 73, 7971)-Net in Base 81 — Upper bound on s

There is no (14, 73, 7972)-net in base 81, because

1 times m-reduction [i] would yield (14, 72, 7972)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 257741 543721 210626 237447 352802 250793 105458 337445 133266 924309 808389 115139 689535 407879 555380 447975 413067 851229 639029 083711 981811 366374 642241 > 81⁷² [i]