MinT - Best Known (75, 172, s)-Nets in Base 4

Best Known (75, 172, s)-Nets in Base 4

(75, 172, 104)-Net over F₄ — Constructive and digital

Digital (75, 172, 104)-net over F₄, using

t-expansion [i] based on digital (73, 172, 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]

(75, 172, 112)-Net over F₄ — Digital

Digital (75, 172, 112)-net over F₄, using

t-expansion [i] based on digital (73, 172, 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]

(75, 172, 833)-Net in Base 4 — Upper bound on s

There is no (75, 172, 834)-net in base 4, because

1 times m-reduction [i] would yield (75, 171, 834)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 388117 677948 236116 367851 597541 104971 477829 627308 296613 181717 248002 506826 874512 380732 369515 397072 717324 > 4¹⁷¹ [i]