MinT - Best Known (254−161, 254, s)-Nets in Base 4

Best Known (254−161, 254, s)-Nets in Base 4

(254−161, 254, 104)-Net over F₄ — Constructive and digital

Digital (93, 254, 104)-net over F₄, using

t-expansion [i] based on digital (73, 254, 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]

(254−161, 254, 144)-Net over F₄ — Digital

Digital (93, 254, 144)-net over F₄, using

t-expansion [i] based on digital (91, 254, 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]

(254−161, 254, 753)-Net in Base 4 — Upper bound on s

There is no (93, 254, 754)-net in base 4, because

1 times m-reduction [i] would yield (93, 253, 754)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 220 850885 931315 743037 961706 419572 866738 089560 253540 251118 810325 578027 071836 778813 228912 298710 291914 385961 695375 445782 795667 808725 198610 874683 166287 722111 > 4²⁵³ [i]