MinT - Best Known (260−165, 260, s)-Nets in Base 4

Best Known (260−165, 260, s)-Nets in Base 4

(260−165, 260, 104)-Net over F₄ — Constructive and digital

Digital (95, 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]

(260−165, 260, 144)-Net over F₄ — Digital

Digital (95, 260, 144)-net over F₄, using

t-expansion [i] based on digital (91, 260, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(260−165, 260, 767)-Net in Base 4 — Upper bound on s

There is no (95, 260, 768)-net in base 4, because

1 times m-reduction [i] would yield (95, 259, 768)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 943235 380524 748815 490339 165423 594563 100855 008315 315622 629943 682461 127175 816138 428632 418864 425296 812317 617971 552741 946233 869486 500722 587727 128085 030691 535021 > 4²⁵⁹ [i]