MinT - Best Known (233−135, 233, s)-Nets in Base 4

Best Known (233−135, 233, s)-Nets in Base 4

(233−135, 233, 104)-Net over F₄ — Constructive and digital

Digital (98, 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]

(233−135, 233, 144)-Net over F₄ — Digital

Digital (98, 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]

(233−135, 233, 990)-Net in Base 4 — Upper bound on s

There is no (98, 233, 991)-net in base 4, because

1 times m-reduction [i] would yield (98, 232, 991)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49 293926 772690 083146 266631 073556 031641 563711 344498 810762 574497 298639 478715 375671 819396 438208 995511 815277 202964 305610 449630 737839 751642 622632 > 4²³² [i]