MinT - Best Known (225−149, 225, s)-Nets in Base 4

Best Known (225−149, 225, s)-Nets in Base 4

(225−149, 225, 104)-Net over F₄ — Constructive and digital

Digital (76, 225, 104)-net over F₄, using

t-expansion [i] based on digital (73, 225, 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]

(225−149, 225, 112)-Net over F₄ — Digital

Digital (76, 225, 112)-net over F₄, using

t-expansion [i] based on digital (73, 225, 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]

(225−149, 225, 569)-Net in Base 4 — Upper bound on s

There is no (76, 225, 570)-net in base 4, because

1 times m-reduction [i] would yield (76, 224, 570)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 772 512657 712019 737960 616749 717367 287684 962287 795133 175229 879138 743232 746229 171586 169658 192085 300065 918984 490375 698103 181663 797642 472192 > 4²²⁴ [i]