MinT - Best Known (185−93, 185, s)-Nets in Base 4

Best Known (185−93, 185, s)-Nets in Base 4

(185−93, 185, 104)-Net over F₄ — Constructive and digital

Digital (92, 185, 104)-net over F₄, using

t-expansion [i] based on digital (73, 185, 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]

(185−93, 185, 144)-Net over F₄ — Digital

Digital (92, 185, 144)-net over F₄, using

t-expansion [i] based on digital (91, 185, 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]

(185−93, 185, 1498)-Net in Base 4 — Upper bound on s

There is no (92, 185, 1499)-net in base 4, because

1 times m-reduction [i] would yield (92, 184, 1499)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 612 720148 588980 825929 094472 512680 250942 389027 433254 284978 340160 913310 640291 809112 538407 108641 303715 601486 065928 > 4¹⁸⁴ [i]