MinT - Best Known (233−132, 233, s)-Nets in Base 4

Best Known (233−132, 233, s)-Nets in Base 4

(233−132, 233, 104)-Net over F₄ — Constructive and digital

Digital (101, 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]

(233−132, 233, 144)-Net over F₄ — Digital

Digital (101, 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]

(233−132, 233, 1077)-Net in Base 4 — Upper bound on s

There is no (101, 233, 1078)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 197 650200 064926 622046 840437 735848 915774 207594 031719 593590 179581 193262 811087 142378 439701 109340 814876 016564 804712 406167 664809 130743 741456 394400 > 4²³³ [i]