MinT - Best Known (200−125, 200, s)-Nets in Base 4

Best Known (200−125, 200, s)-Nets in Base 4

(200−125, 200, 104)-Net over F₄ — Constructive and digital

Digital (75, 200, 104)-net over F₄, using

t-expansion [i] based on digital (73, 200, 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]

(200−125, 200, 112)-Net over F₄ — Digital

Digital (75, 200, 112)-net over F₄, using

t-expansion [i] based on digital (73, 200, 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]

(200−125, 200, 633)-Net in Base 4 — Upper bound on s

There is no (75, 200, 634)-net in base 4, because

1 times m-reduction [i] would yield (75, 199, 634)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 704078 324366 244888 637926 210957 741105 979153 607466 023266 820254 018296 656374 418169 079587 040108 180833 831587 064470 537209 181920 > 4¹⁹⁹ [i]