MinT - Best Known (208−106, 208, s)-Nets in Base 4

Best Known (208−106, 208, s)-Nets in Base 4

(208−106, 208, 104)-Net over F₄ — Constructive and digital

Digital (102, 208, 104)-net over F₄, using

t-expansion [i] based on digital (73, 208, 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]

(208−106, 208, 144)-Net over F₄ — Digital

Digital (102, 208, 144)-net over F₄, using

t-expansion [i] based on digital (91, 208, 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]

(208−106, 208, 1539)-Net in Base 4 — Upper bound on s

There is no (102, 208, 1540)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 170640 811826 994825 166075 240160 687389 494630 313360 092434 287522 420167 840969 359098 282013 028885 525288 133237 270143 660248 136722 784640 > 4²⁰⁸ [i]