MinT - Best Known (150−75, 150, s)-Nets in Base 4

Best Known (150−75, 150, s)-Nets in Base 4

(150−75, 150, 104)-Net over F₄ — Constructive and digital

Digital (75, 150, 104)-net over F₄, using

t-expansion [i] based on digital (73, 150, 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]

(150−75, 150, 112)-Net over F₄ — Digital

Digital (75, 150, 112)-net over F₄, using

t-expansion [i] based on digital (73, 150, 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]

(150−75, 150, 1268)-Net in Base 4 — Upper bound on s

There is no (75, 150, 1269)-net in base 4, because

1 times m-reduction [i] would yield (75, 149, 1269)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 523710 638307 767072 773475 950432 996149 224851 099766 313715 456285 973856 713859 363354 447142 773220 > 4¹⁴⁹ [i]