MinT - Best Known (174−99, 174, s)-Nets in Base 4

Best Known (174−99, 174, s)-Nets in Base 4

(174−99, 174, 104)-Net over F₄ — Constructive and digital

Digital (75, 174, 104)-net over F₄, using

t-expansion [i] based on digital (73, 174, 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]

(174−99, 174, 112)-Net over F₄ — Digital

Digital (75, 174, 112)-net over F₄, using

t-expansion [i] based on digital (73, 174, 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]

(174−99, 174, 811)-Net in Base 4 — Upper bound on s

There is no (75, 174, 812)-net in base 4, because

1 times m-reduction [i] would yield (75, 173, 812)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 150 275415 868867 189259 112466 834904 522896 578587 848558 705289 263792 373274 716369 880517 555767 104563 449755 629840 > 4¹⁷³ [i]