MinT - Best Known (75, 170, s)-Nets in Base 4

Best Known (75, 170, s)-Nets in Base 4

(75, 170, 104)-Net over F₄ — Constructive and digital

Digital (75, 170, 104)-net over F₄, using

t-expansion [i] based on digital (73, 170, 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, 170, 112)-Net over F₄ — Digital

Digital (75, 170, 112)-net over F₄, using

t-expansion [i] based on digital (73, 170, 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, 170, 856)-Net in Base 4 — Upper bound on s

There is no (75, 170, 857)-net in base 4, because

1 times m-reduction [i] would yield (75, 169, 857)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 560609 439558 269883 602282 974067 926468 163404 793724 724535 134697 998612 993230 291401 016735 836679 429736 141600 > 4¹⁶⁹ [i]