MinT - Best Known (124−75, 124, s)-Nets in Base 3

Best Known (124−75, 124, s)-Nets in Base 3

(124−75, 124, 48)-Net over F₃ — Constructive and digital

Digital (49, 124, 48)-net over F₃, using

t-expansion [i] based on digital (45, 124, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(124−75, 124, 64)-Net over F₃ — Digital

Digital (49, 124, 64)-net over F₃, using

net from sequence [i] based on digital (49, 63)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
  - a curve from the manYPoints database [i]

(124−75, 124, 247)-Net in Base 3 — Upper bound on s

There is no (49, 124, 248)-net in base 3, because

1 times m-reduction [i] would yield (49, 123, 248)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 49683 542082 428075 066746 217084 036746 410056 251377 339630 579057 > 3¹²³ [i]