MinT - Best Known (223−121, 223, s)-Nets in Base 4

Best Known (223−121, 223, s)-Nets in Base 4

(223−121, 223, 104)-Net over F₄ — Constructive and digital

Digital (102, 223, 104)-net over F₄, using

t-expansion [i] based on digital (73, 223, 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]

(223−121, 223, 144)-Net over F₄ — Digital

Digital (102, 223, 144)-net over F₄, using

t-expansion [i] based on digital (91, 223, 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]

(223−121, 223, 1256)-Net in Base 4 — Upper bound on s

There is no (102, 223, 1257)-net in base 4, because

1 times m-reduction [i] would yield (102, 222, 1257)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45 671119 003021 250781 231906 147096 520052 051613 703950 076013 771225 786948 381097 253254 070600 054673 345110 949284 288922 571531 104217 366122 807440 > 4²²² [i]