MinT - Best Known (233−153, 233, s)-Nets in Base 4

Best Known (233−153, 233, s)-Nets in Base 4

(233−153, 233, 104)-Net over F₄ — Constructive and digital

Digital (80, 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]

(233−153, 233, 112)-Net over F₄ — Digital

Digital (80, 233, 112)-net over F₄, using

t-expansion [i] based on digital (73, 233, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(233−153, 233, 607)-Net in Base 4 — Upper bound on s

There is no (80, 233, 608)-net in base 4, because

1 times m-reduction [i] would yield (80, 232, 608)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50 429384 454918 305291 858738 933435 490061 224377 163384 787154 707406 810474 337643 070721 356555 796259 825660 359580 215147 193034 037801 259826 937689 148625 > 4²³² [i]