MinT - Best Known (234−131, 234, s)-Nets in Base 4

Best Known (234−131, 234, s)-Nets in Base 4

(234−131, 234, 104)-Net over F₄ — Constructive and digital

Digital (103, 234, 104)-net over F₄, using

t-expansion [i] based on digital (73, 234, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(234−131, 234, 144)-Net over F₄ — Digital

Digital (103, 234, 144)-net over F₄, using

t-expansion [i] based on digital (91, 234, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(234−131, 234, 1148)-Net in Base 4 — Upper bound on s

There is no (103, 234, 1149)-net in base 4, because

1 times m-reduction [i] would yield (103, 233, 1149)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 192 751361 721448 071638 899544 337384 529210 231780 257181 052654 252622 893831 760409 354091 949766 355064 523982 167873 437278 750825 332445 937632 839329 572776 > 4²³³ [i]