MinT - Best Known (260−181, 260, s)-Nets in Base 4

Best Known (260−181, 260, s)-Nets in Base 4

(260−181, 260, 104)-Net over F₄ — Constructive and digital

Digital (79, 260, 104)-net over F₄, using

t-expansion [i] based on digital (73, 260, 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]

(260−181, 260, 112)-Net over F₄ — Digital

Digital (79, 260, 112)-net over F₄, using

t-expansion [i] based on digital (73, 260, 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]

(260−181, 260, 546)-Net in Base 4 — Upper bound on s

There is no (79, 260, 547)-net in base 4, because

1 times m-reduction [i] would yield (79, 259, 547)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 945380 715782 276182 199983 554000 457148 476601 443792 494824 340577 356740 958498 190271 674711 130849 092634 479586 751811 458908 382368 605876 008654 665408 746583 283341 843488 > 4²⁵⁹ [i]