MinT - Best Known (223−126, 223, s)-Nets in Base 4

Best Known (223−126, 223, s)-Nets in Base 4

(223−126, 223, 104)-Net over F₄ — Constructive and digital

Digital (97, 223, 104)-net over F₄, using

t-expansion [i] based on digital (73, 223, 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]

(223−126, 223, 144)-Net over F₄ — Digital

Digital (97, 223, 144)-net over F₄, using

t-expansion [i] based on digital (91, 223, 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]

(223−126, 223, 1044)-Net in Base 4 — Upper bound on s

There is no (97, 223, 1045)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 186 844656 813839 410385 291620 825154 514634 672882 509843 452970 669837 282213 681015 381285 621271 285818 473139 888438 958259 531703 767439 382856 350720 > 4²²³ [i]