MinT - Best Known (92, 223, s)-Nets in Base 4

Best Known (92, 223, s)-Nets in Base 4

(92, 223, 104)-Net over F₄ — Constructive and digital

Digital (92, 223, 104)-net over F₄, using

t-expansion [i] based on digital (73, 223, 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]

(92, 223, 144)-Net over F₄ — Digital

Digital (92, 223, 144)-net over F₄, using

t-expansion [i] based on digital (91, 223, 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]

(92, 223, 897)-Net in Base 4 — Upper bound on s

There is no (92, 223, 898)-net in base 4, because

1 times m-reduction [i] would yield (92, 222, 898)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46 207697 236799 868731 044304 192217 220164 103803 470107 238001 792038 488554 176814 153657 081591 278841 911491 340766 451370 068169 419947 195245 357206 > 4²²² [i]