MinT - Best Known (193−99, 193, s)-Nets in Base 4

Best Known (193−99, 193, s)-Nets in Base 4

(193−99, 193, 104)-Net over F₄ — Constructive and digital

Digital (94, 193, 104)-net over F₄, using

t-expansion [i] based on digital (73, 193, 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]

(193−99, 193, 144)-Net over F₄ — Digital

Digital (94, 193, 144)-net over F₄, using

t-expansion [i] based on digital (91, 193, 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]

(193−99, 193, 1416)-Net in Base 4 — Upper bound on s

There is no (94, 193, 1417)-net in base 4, because

1 times m-reduction [i] would yield (94, 192, 1417)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40 093352 245540 020693 606786 891920 537553 753497 735827 706432 413562 960473 118265 393482 893211 148263 574113 099098 932260 477152 > 4¹⁹² [i]