MinT - Best Known (260−164, 260, s)-Nets in Base 4

Best Known (260−164, 260, s)-Nets in Base 4

(260−164, 260, 104)-Net over F₄ — Constructive and digital

Digital (96, 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]

(260−164, 260, 144)-Net over F₄ — Digital

Digital (96, 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]

(260−164, 260, 781)-Net in Base 4 — Upper bound on s

There is no (96, 260, 782)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 706313 196502 325230 808837 559959 003790 874001 186832 561088 603909 343790 466741 963045 759635 634341 851022 644431 887334 366659 775660 302698 390734 764725 683912 062281 260960 > 4²⁶⁰ [i]