MinT - Best Known (223−147, 223, s)-Nets in Base 4

Best Known (223−147, 223, s)-Nets in Base 4

(223−147, 223, 104)-Net over F₄ — Constructive and digital

Digital (76, 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]

(223−147, 223, 112)-Net over F₄ — Digital

Digital (76, 223, 112)-net over F₄, using

t-expansion [i] based on digital (73, 223, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(223−147, 223, 574)-Net in Base 4 — Upper bound on s

There is no (76, 223, 575)-net in base 4, because

1 times m-reduction [i] would yield (76, 222, 575)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49 454021 002411 338997 441034 894259 265839 570433 131594 609011 350076 548749 997439 456439 018978 825423 221587 281433 023924 646953 578014 619176 631728 > 4²²² [i]