MinT - Best Known (221−140, 221, s)-Nets in Base 4

Best Known (221−140, 221, s)-Nets in Base 4

(221−140, 221, 104)-Net over F₄ — Constructive and digital

Digital (81, 221, 104)-net over F₄, using

t-expansion [i] based on digital (73, 221, 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]

(221−140, 221, 129)-Net over F₄ — Digital

Digital (81, 221, 129)-net over F₄, using

net from sequence [i] based on digital (81, 128)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
  - Drinfeld modules of rank 1 [i]

(221−140, 221, 657)-Net in Base 4 — Upper bound on s

There is no (81, 221, 658)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 133686 242390 973546 956939 132486 764614 775440 748799 517961 213114 195480 333592 642679 208806 923294 721443 102982 335107 388449 021446 257361 020560 > 4²²¹ [i]