MinT - Best Known (194−97, 194, s)-Nets in Base 4

Best Known (194−97, 194, s)-Nets in Base 4

(194−97, 194, 104)-Net over F₄ — Constructive and digital

Digital (97, 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]

(194−97, 194, 144)-Net over F₄ — Digital

Digital (97, 194, 144)-net over F₄, using

t-expansion [i] based on 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]

(194−97, 194, 1606)-Net in Base 4 — Upper bound on s

There is no (97, 194, 1607)-net in base 4, because

1 times m-reduction [i] would yield (97, 193, 1607)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 157 884257 628216 694708 520754 081336 045045 546336 235749 558555 547769 805644 302171 741808 038956 523138 412229 597965 517279 628492 > 4¹⁹³ [i]