MinT - Best Known (75, 168, s)-Nets in Base 4

Best Known (75, 168, s)-Nets in Base 4

(75, 168, 104)-Net over F₄ — Constructive and digital

Digital (75, 168, 104)-net over F₄, using

t-expansion [i] based on digital (73, 168, 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, 168, 112)-Net over F₄ — Digital

Digital (75, 168, 112)-net over F₄, using

t-expansion [i] based on digital (73, 168, 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, 168, 882)-Net in Base 4 — Upper bound on s

There is no (75, 168, 883)-net in base 4, because

1 times m-reduction [i] would yield (75, 167, 883)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35211 665020 894312 806104 100806 847346 217645 071444 285768 152624 940652 311110 307026 409522 198642 974844 437940 > 4¹⁶⁷ [i]