MinT - Best Known (245−153, 245, s)-Nets in Base 4

Best Known (245−153, 245, s)-Nets in Base 4

(245−153, 245, 104)-Net over F₄ — Constructive and digital

Digital (92, 245, 104)-net over F₄, using

t-expansion [i] based on digital (73, 245, 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]

(245−153, 245, 144)-Net over F₄ — Digital

Digital (92, 245, 144)-net over F₄, using

t-expansion [i] based on digital (91, 245, 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]

(245−153, 245, 770)-Net in Base 4 — Upper bound on s

There is no (92, 245, 771)-net in base 4, because

1 times m-reduction [i] would yield (92, 244, 771)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 829 493512 745462 437197 970223 207206 986974 298270 998990 970283 196844 417075 084638 104397 051180 478895 816285 971181 708349 658723 700985 864140 404164 017210 689856 > 4²⁴⁴ [i]