MinT - Best Known (233−137, 233, s)-Nets in Base 4

Best Known (233−137, 233, s)-Nets in Base 4

(233−137, 233, 104)-Net over F₄ — Constructive and digital

Digital (96, 233, 104)-net over F₄, using

t-expansion [i] based on digital (73, 233, 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]

(233−137, 233, 144)-Net over F₄ — Digital

Digital (96, 233, 144)-net over F₄, using

t-expansion [i] based on digital (91, 233, 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]

(233−137, 233, 932)-Net in Base 4 — Upper bound on s

There is no (96, 233, 933)-net in base 4, because

1 times m-reduction [i] would yield (96, 232, 933)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49 289179 073723 567558 112911 116674 706808 468239 113779 927770 397814 422056 460250 099100 913972 656575 453798 623446 718793 919764 218005 090773 206554 586590 > 4²³² [i]