MinT - Best Known (249−174, 249, s)-Nets in Base 4

Best Known (249−174, 249, s)-Nets in Base 4

(249−174, 249, 104)-Net over F₄ — Constructive and digital

Digital (75, 249, 104)-net over F₄, using

t-expansion [i] based on digital (73, 249, 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]

(249−174, 249, 112)-Net over F₄ — Digital

Digital (75, 249, 112)-net over F₄, using

t-expansion [i] based on digital (73, 249, 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]

(249−174, 249, 515)-Net in Base 4 — Upper bound on s

There is no (75, 249, 516)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 825789 268601 174634 685601 982839 594251 632408 494273 259391 369649 682821 895513 155161 574831 860157 255709 965216 509127 037035 949741 359400 169127 314605 206774 550400 > 4²⁴⁹ [i]