MinT - Best Known (235−138, 235, s)-Nets in Base 4

Best Known (235−138, 235, s)-Nets in Base 4

(235−138, 235, 104)-Net over F₄ — Constructive and digital

Digital (97, 235, 104)-net over F₄, using

t-expansion [i] based on digital (73, 235, 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]

(235−138, 235, 144)-Net over F₄ — Digital

Digital (97, 235, 144)-net over F₄, using

t-expansion [i] based on digital (91, 235, 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]

(235−138, 235, 937)-Net in Base 4 — Upper bound on s

There is no (97, 235, 938)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3172 071376 133756 853023 796306 860195 230828 156882 593680 999317 732449 933440 465652 854562 835773 155786 280409 016825 865662 963475 331150 375732 166965 465900 > 4²³⁵ [i]