MinT - Best Known (220−144, 220, s)-Nets in Base 4

Best Known (220−144, 220, s)-Nets in Base 4

(220−144, 220, 104)-Net over F₄ — Constructive and digital

Digital (76, 220, 104)-net over F₄, using

t-expansion [i] based on digital (73, 220, 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]

(220−144, 220, 112)-Net over F₄ — Digital

Digital (76, 220, 112)-net over F₄, using

t-expansion [i] based on digital (73, 220, 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]

(220−144, 220, 579)-Net in Base 4 — Upper bound on s

There is no (76, 220, 580)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 070995 455542 409091 521649 908510 240233 938854 267879 977935 822149 895281 768073 813155 431467 427168 329942 221378 308289 154386 991737 418437 083840 > 4²²⁰ [i]