MinT - Best Known (233−139, 233, s)-Nets in Base 4

Best Known (233−139, 233, s)-Nets in Base 4

(233−139, 233, 104)-Net over F₄ — Constructive and digital

Digital (94, 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]

(233−139, 233, 144)-Net over F₄ — Digital

Digital (94, 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]

(233−139, 233, 879)-Net in Base 4 — Upper bound on s

There is no (94, 233, 880)-net in base 4, because

1 times m-reduction [i] would yield (94, 232, 880)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49 772247 528549 559014 092666 491618 752464 337625 335516 048624 313185 240046 203593 346881 345017 450146 117980 396649 621629 602156 796319 621553 222031 241799 > 4²³² [i]