MinT - Best Known (194−103, 194, s)-Nets in Base 4

Best Known (194−103, 194, s)-Nets in Base 4

(194−103, 194, 104)-Net over F₄ — Constructive and digital

Digital (91, 194, 104)-net over F₄, using

t-expansion [i] based on digital (73, 194, 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]

(194−103, 194, 144)-Net over F₄ — Digital

Digital (91, 194, 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]

(194−103, 194, 1214)-Net in Base 4 — Upper bound on s

There is no (91, 194, 1215)-net in base 4, because

1 times m-reduction [i] would yield (91, 193, 1215)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 158 247519 721412 837680 741149 810782 090196 414039 534817 908232 888552 374128 486440 828234 142531 958656 285180 950134 850248 444280 > 4¹⁹³ [i]