MinT - Best Known (245−131, 245, s)-Nets in Base 4

Best Known (245−131, 245, s)-Nets in Base 4

(245−131, 245, 130)-Net over F₄ — Constructive and digital

Digital (114, 245, 130)-net over F₄, using

t-expansion [i] based on digital (105, 245, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(245−131, 245, 165)-Net over F₄ — Digital

Digital (114, 245, 165)-net over F₄, using

t-expansion [i] based on digital (109, 245, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(245−131, 245, 1466)-Net in Base 4 — Upper bound on s

There is no (114, 245, 1467)-net in base 4, because

1 times m-reduction [i] would yield (114, 244, 1467)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 823 325029 300779 223952 343958 387309 486783 674699 934832 903185 301389 859110 969900 602770 085108 072411 620629 407992 126252 646502 581977 613569 698853 476685 684380 > 4²⁴⁴ [i]