MinT - Best Known (255−161, 255, s)-Nets in Base 4

Best Known (255−161, 255, s)-Nets in Base 4

(255−161, 255, 104)-Net over F₄ — Constructive and digital

Digital (94, 255, 104)-net over F₄, using

t-expansion [i] based on digital (73, 255, 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]

(255−161, 255, 144)-Net over F₄ — Digital

Digital (94, 255, 144)-net over F₄, using

t-expansion [i] based on digital (91, 255, 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]

(255−161, 255, 767)-Net in Base 4 — Upper bound on s

There is no (94, 255, 768)-net in base 4, because

1 times m-reduction [i] would yield (94, 254, 768)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 860 747419 380628 475415 049232 370315 905908 088915 171136 285738 959352 967647 308683 056805 838806 207608 164292 955132 067965 745927 659996 226462 313774 441816 350017 169197 > 4²⁵⁴ [i]